From 88a081ff6aede20726ac3d594d7c86cb36fd894e Mon Sep 17 00:00:00 2001 From: Melanie Date: Mon, 13 Nov 2023 10:42:23 -0500 Subject: [PATCH 01/15] Resuscitate the Cloudy example---this is a working but not cleaned-up version --- examples/deprecated/Cloudy/Cloudy_example.jl | 297 +++++++++++++------ examples/deprecated/Cloudy/DynamicalModel.jl | 120 ++++++++ examples/deprecated/Cloudy/GModel.jl | 116 -------- examples/deprecated/Cloudy/Project.toml | 1 - 4 files changed, 325 insertions(+), 209 deletions(-) create mode 100644 examples/deprecated/Cloudy/DynamicalModel.jl delete mode 100644 examples/deprecated/Cloudy/GModel.jl diff --git a/examples/deprecated/Cloudy/Cloudy_example.jl b/examples/deprecated/Cloudy/Cloudy_example.jl index 75bc41e65..b1b901084 100644 --- a/examples/deprecated/Cloudy/Cloudy_example.jl +++ b/examples/deprecated/Cloudy/Cloudy_example.jl @@ -1,25 +1,41 @@ # Reference the in-tree version of CalibrateEmulateSample on Julias load path +include(joinpath(@__DIR__, "../..", "ci", "linkfig.jl")) +include(joinpath(@__DIR__, "DynamicalModel.jl")) # Import the module that runs Cloudy -include(joinpath(@__DIR__, "..", "ci", "linkfig.jl")) -include(joinpath(@__DIR__, "GModel.jl")) # Import the module that runs Cloudy +# This example requires Cloudy to be installed (it's best to install the master +# branch), which can be done by: +#] add Cloudy#master +using Cloudy +using Cloudy.ParticleDistributions +using Cloudy.KernelTensors + +# Import the module that runs Cloudy +#include("DynamicalModel.jl") +#using .DynamicalModel # Import modules using Distributions # probability distributions and associated functions using StatsBase +using GaussianProcesses using LinearAlgebra using StatsPlots -using GaussianProcesses using Plots +using Plots.PlotMeasures # is this needed? using Random +using JLD2 # is this needed? # Import Calibrate-Emulate-Sample modules -using CalibrateEmulateSample.EnsembleKalmanProcesses +# For the calibration step we use the EnsembleKalmanProcesses package, and +# for the sampling we use Markov chain Monte Carlo methods. We'll +# run this example twice, using first a Gaussian process emulator, and +# then a Random Feature emulator. +using EnsembleKalmanProcesses +using EnsembleKalmanProcesses.Observations +using EnsembleKalmanProcesses.ParameterDistributions +using EnsembleKalmanProcesses.DataContainers using CalibrateEmulateSample.Emulators using CalibrateEmulateSample.MarkovChainMonteCarlo using CalibrateEmulateSample.Utilities -using CalibrateEmulateSample.ParameterDistributions -using CalibrateEmulateSample.DataContainers -using CalibrateEmulateSample.Observations # This example requires Cloudy to be installed. using Cloudy @@ -58,10 +74,16 @@ const PDistributions = Cloudy.ParticleDistributions rng_seed = 41 Random.seed!(rng_seed) +rng = Random.seed!(Random.GLOBAL_RNG, rng_seed) -output_directory = joinpath(@__DIR__, "output") -if !isdir(output_directory) - mkdir(output_directory) +homedir = pwd() +figure_save_directory = homedir * "/output/" +data_save_directory = homedir * "/output/" +if ~isdir(figure_save_directory) + mkdir(figure_save_directory) +end +if ~isdir(data_save_directory) + mkdir(data_save_directory) end ### @@ -69,43 +91,29 @@ end ### # Define the parameters that we want to learn -# We assume that the true particle mass distribution is a Gamma distribution -# with parameters N0_true, θ_true, k_true -param_names = ["N0", "θ", "k"] -n_param = length(param_names) - +# We assume that the true particle mass distribution is a Gamma +# distribution with parameters N0_true, θ_true, k_true +par_names = ["N0", "θ", "k"] +n_par = length(par_names) N0_true = 300.0 # number of particles (scaling factor for Gamma distribution) θ_true = 1.5597 # scale parameter of Gamma distribution k_true = 0.0817 # shape parameter of Gamma distribution -params_true = [N0_true, θ_true, k_true] # Note that dist_true is a Cloudy distribution, not a Distributions.jl # distribution -dist_true = PDistributions.Gamma(N0_true, θ_true, k_true) +ϕ_true = [N0_true, θ_true, k_true] +dist_true = ParticleDistributions.GammaPrimitiveParticleDistribution(ϕ_true...) ### ### Define priors for the parameters we want to learn ### -# Define constraints -lbound_N0 = 0.4 * N0_true -lbound_θ = 1.0e-1 -lbound_k = 1.0e-4 -c1 = bounded_below(lbound_N0) -c2 = bounded_below(lbound_θ) -c3 = bounded_below(lbound_k) -constraints = [[c1], [c2], [c3]] - # We choose to use normal distributions to represent the prior distributions of # the parameters in the transformed (unconstrained) space. i.e log coordinates -d1 = Parameterized(Normal(4.5, 1.0)) #truth is 5.19 -d2 = Parameterized(Normal(0.0, 2.0)) #truth is 0.378 -d3 = Parameterized(Normal(-1.0, 1.0))#truth is -2.51 -distributions = [d1, d2, d3] - -param_names = ["N0", "θ", "k"] - -priors = ParameterDistribution(distributions, constraints, param_names) +prior_N0 = constrained_gaussian(par_names[1], 400, 300, 0.4 * N0_true, Inf) +prior_θ = constrained_gaussian(par_names[2], 1.0, 5.0, 1e-1, Inf) +prior_k = constrained_gaussian(par_names[3], 0.2, 1.0, 1e-4, Inf) +priors = combine_distributions([prior_N0, prior_θ, prior_k]) ### ### Define the data from which we want to learn the parameters @@ -121,100 +129,205 @@ n_moments = length(moments) ### # Collision-coalescence kernel to be used in Cloudy +tspan = (0.0, 1.0) +print("tspan ", tspan) coalescence_coeff = 1 / 3.14 / 4 / 100 kernel_func = x -> coalescence_coeff -kernel = Cloudy.KernelTensors.CoalescenceTensor(kernel_func, 0, 100.0) - -# Time period over which to run Cloudy -tspan = (0.0, 1.0) +kernel = Cloudy.KernelTensors.CoalescenceTensor(kernel_func, 0, 300.0) ### ### Generate (artificial) truth samples -### Note: The observables y are related to the parameters θ by: -### y = G(x1, x2) + η ### -g_settings_true = GModel.GSettings(kernel, dist_true, moments, tspan) -gt = GModel.run_G( - params_true, - g_settings_true, - PDistributions.update_params, - PDistributions.moment, - Cloudy.Sources.get_int_coalescence, -) +dyn_model_settings_true = DynamicalModel.ModelSettings(kernel, dist_true, moments, tspan) + +G_t = DynamicalModel.run_dyn_model(ϕ_true, dyn_model_settings_true) n_samples = 100 -yt = zeros(length(gt), n_samples) -# In a perfect model setting, the "observational noise" represent the internal -# model variability. Since Cloudy is a purely deterministic model, there is no -# straightforward way of coming up with a covariance structure for this internal -# model variability. We decide to use a diagonal covariance, with entries -# (variances) largely proportional to their corresponding data values, gt. +y_t = zeros(length(G_t), n_samples) +# In a perfect model setting, the "observational noise" represents the +# internal model variability. Since Cloudy is a purely deterministic model, +# there is no straightforward way of coming up with a covariance structure +# for this internal model variability. We decide to use a diagonal +# covariance, with entries (variances) largely proportional to their +# corresponding data values, G_t Γy = convert(Array, Diagonal([100.0, 5.0, 30.0])) -μ = zeros(length(gt)) +μ = zeros(length(G_t)) # Add noise for i in 1:n_samples - yt[:, i] = gt .+ rand(MvNormal(μ, Γy)) + y_t[:, i] = G_t .+ rand(MvNormal(μ, Γy)) end -truth = Observations.Observation(yt, Γy, data_names) +truth = Observations.Observation(y_t, Γy, data_names) truth_sample = truth.mean + + ### ### Calibrate: Ensemble Kalman Inversion ### - N_ens = 50 # number of ensemble members N_iter = 8 # number of EKI iterations -# initial parameters: N_params x N_ens -initial_params = EnsembleKalmanProcesses.construct_initial_ensemble(priors, N_ens; rng_seed = 6) -ekiobj = EnsembleKalmanProcesses.EnsembleKalmanProcess( - initial_params, +# initial parameters: N_par x N_ens +initial_par = construct_initial_ensemble(rng, priors, N_ens) +ekiobj = EnsembleKalmanProcess( + initial_par, truth_sample, truth.obs_noise_cov, Inversion(), - Δt = 0.1, ) - # Initialize a ParticleDistribution with dummy parameters. The parameters -# will then be set in run_G_ensemble -dummy = 1.0 -dist_type = PDistributions.Gamma(dummy, dummy, dummy) -g_settings = GModel.GSettings(kernel, dist_type, moments, tspan) - +# will then be set within `run_dyn_model` +dummy = ones(n_par) +dist_type = ParticleDistributions.GammaPrimitiveParticleDistribution(dummy...) +model_settings = DynamicalModel.ModelSettings(kernel, dist_type, moments, tspan) # EKI iterations -for i in 1:N_iter - params_i = mapslices(x -> transform_unconstrained_to_constrained(priors, x), get_u_final(ekiobj); dims = 1) - g_ens = GModel.run_G_ensemble( - params_i, - g_settings, - PDistributions.update_params, - PDistributions.moment, - Cloudy.Sources.get_int_coalescence, - ) - EnsembleKalmanProcesses.update_ensemble!(ekiobj, g_ens) +for n in 1:N_iter + # Return transformed parameters in physical/constrained space + ϕ_n = get_ϕ_final(priors, ekiobj) + # Evaluate forward map + G_n = [DynamicalModel.run_dyn_model(ϕ_n[:, i], model_settings) for i in 1:N_ens] + G_ens = hcat(G_n...) # reformat + EnsembleKalmanProcesses.update_ensemble!(ekiobj, G_ens) end # EKI results: Has the ensemble collapsed toward the truth? -transformed_params_true = transform_constrained_to_unconstrained(priors, params_true) -println("True parameters (transformed): ") -println(transformed_params_true) +θ_true = transform_constrained_to_unconstrained(priors, ϕ_true) +println("True parameters (unconstrained): ") +println(θ_true) println("\nEKI results:") -println(mean(get_u_final(ekiobj), dims = 2)) +println(get_u_mean_final(ekiobj)) + +u_stored = get_u(ekiobj, return_array = false) +g_stored = get_g(ekiobj, return_array = false) +@save data_save_directory * "parameter_storage_eki.jld2" u_stored +@save data_save_directory * "data_storage_eki.jld2" g_stored + +#plots - unconstrained +gr(size = (1200, 400)) + +u_init = get_u_prior(ekiobj) +anim_eki_unconst_cloudy = @animate for i in 1:N_iter + u_i = get_u(ekiobj, i) + + p1 = plot(u_i[1, :], u_i[2, :], seriestype = :scatter, xlims = extrema(u_init[1, :]), ylims = extrema(u_init[2, :])) + plot!( + p1, + [θ_true[1]], + xaxis = "u1", + yaxis = "u2", + seriestype = "vline", + linestyle = :dash, + linecolor = :red, + label = false, + margin = 5mm, + title = "EKI iteration = " * string(i), + ) + plot!(p1, [θ_true[2]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") + + p2 = plot(u_i[2, :], u_i[3, :], seriestype = :scatter, xlims = extrema(u_init[2, :]), ylims = extrema(u_init[3, :])) + plot!( + p2, + [θ_true[2]], + xaxis = "u2", + yaxis = "u3", + seriestype = "vline", + linestyle = :dash, + linecolor = :red, + label = false, + margin = 5mm, + title = "EKI iteration = " * string(i), + ) + plot!(p2, [θ_true[3]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") + + p3 = plot(u_i[3, :], u_i[1, :], seriestype = :scatter, xlims = extrema(u_init[3, :]), ylims = extrema(u_init[1, :])) + plot!( + p3, + [θ_true[3]], + xaxis = "u3", + yaxis = "u1", + seriestype = "vline", + linestyle = :dash, + linecolor = :red, + label = false, + margin = 5mm, + title = "EKI iteration = " * string(i), + ) + plot!(p3, [θ_true[1]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") + + p = plot(p1, p2, p3, layout = (1, 3)) +end +gif(anim_eki_unconst_cloudy, joinpath(figure_save_directory, "eki_unconst_cloudy.gif"), fps = 1) # hide + +# plots - constrained +ϕ_init = transform_unconstrained_to_constrained(priors, u_init) +anim_eki_cloudy = @animate for i in 1:N_iter + ϕ_i = get_ϕ(priors, ekiobj, i) + + p1 = plot(ϕ_i[1, :], ϕ_i[2, :], seriestype = :scatter, xlims = extrema(ϕ_init[1, :]), ylims = extrema(ϕ_init[2, :])) + plot!( + p1, + [ϕ_true[1]], + xaxis = "ϕ1", + yaxis = "ϕ2", + seriestype = "vline", + linestyle = :dash, + linecolor = :red, + margin = 5mm, + label = false, + title = "EKI iteration = " * string(i), + ) + plot!(p1, [ϕ_true[2]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") + + p2 = plot(ϕ_i[2, :], ϕ_i[3, :], seriestype = :scatter, xlims = extrema(ϕ_init[2, :]), ylims = extrema(ϕ_init[3, :])) + plot!( + p2, + [ϕ_true[2]], + xaxis = "ϕ2", + yaxis = "ϕ3", + seriestype = "vline", + linestyle = :dash, + linecolor = :red, + margin = 5mm, + label = false, + title = "EKI iteration = " * string(i), + ) + plot!(p2, [ϕ_true[3]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") + + p3 = plot(ϕ_i[3, :], ϕ_i[1, :], seriestype = :scatter, xlims = extrema(ϕ_init[3, :]), ylims = extrema(ϕ_init[1, :])) + plot!( + p3, + [ϕ_true[3]], + xaxis = "ϕ3", + yaxis = "ϕ1", + seriestype = "vline", + linestyle = :dash, + linecolor = :red, + margin = 5mm, + label = false, + title = "EKI iteration = " * string(i), + ) + plot!(p3, [ϕ_true[1]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") + + p = plot(p1, p2, p3, layout = (1, 3)) +end +gif(anim_eki_cloudy, joinpath(figure_save_directory, "eki_cloudy.gif"), fps = 1) # hide ### -### Emulate: Gaussian Process Regression +### Emulate: Gaussian Process regression ### + gppackage = Emulators.GPJL() pred_type = Emulators.YType() +gp_kernel = SE(1.0, 1.0) + Mat52Ard(zeros(3), 0.0) + Noise(log(2.0)) gauss_proc = GaussianProcess( gppackage; - kernel = nothing, # use default squared exponential kernel + kernel = gp_kernel, g use default squared exponential kernel prediction_type = pred_type, noise_learn = false, ) @@ -226,7 +339,7 @@ optimize_hyperparameters!(emulator) # Check how well the Gaussian Process regression predicts on the # true parameters -y_mean, y_var = Emulators.predict(emulator, reshape(transformed_params_true, :, 1); transform_to_real = true) +y_mean, y_var = Emulators.predict(emulator, reshape(θ_true, :, 1); transform_to_real = true) println("GP prediction on true parameters: ") println(vec(y_mean)) println("true data: ") @@ -275,8 +388,8 @@ for idx in 1:n_params throw("not implemented") end - label = "true " * param_names[idx] - posterior_samples = dropdims(get_distribution(posterior)[param_names[idx]], dims = 1) + label = "true " * par_names[idx] + posterior_samples = dropdims(get_distribution(posterior)[par_names[idx]], dims = 1) histogram( posterior_samples, bins = 100, @@ -286,11 +399,11 @@ for idx in 1:n_params lab = "posterior", legend = :outertopright, ) - prior_dist = get_distribution(mcmc.prior)[param_names[idx]] + prior_dist = get_distribution(mcmc.prior)[par_names[idx]] plot!(xs, prior_dist, w = 2.6, color = :blue, lab = "prior") - plot!([transformed_params_true[idx]], seriestype = "vline", w = 2.6, lab = label) - title!(param_names[idx]) - figpath = joinpath(output_directory, "posterior_" * param_names[idx] * ".png") + plot!([θ_true[idx]], seriestype = "vline", w = 2.6, lab = label) + title!(par_names[idx]) + figpath = joinpath(figure_save_directory, "posterior_" * par_names[idx] * ".png") StatsPlots.savefig(figpath) linkfig(figpath) end diff --git a/examples/deprecated/Cloudy/DynamicalModel.jl b/examples/deprecated/Cloudy/DynamicalModel.jl new file mode 100644 index 000000000..7967d694e --- /dev/null +++ b/examples/deprecated/Cloudy/DynamicalModel.jl @@ -0,0 +1,120 @@ +module DynamicalModel + +using DocStringExtensions + +using Cloudy +using Cloudy.ParticleDistributions +using Cloudy.KernelTensors +using Cloudy.EquationTypes +using Cloudy.Coalescence + +using Sundials # CVODE_BDF() solver for ODE + + +using DifferentialEquations + +export ModelSettings +export run_dyn_model + + +""" + ModelSettings{FT<:AbstractFloat, KT, D} + +Structure to hold all information to run the dynamical model + +# Fields +$(DocStringExtensions.FIELDS) +""" +struct ModelSettings{FT <: AbstractFloat, KT, D <: PrimitiveParticleDistribution{FT}} + "a kernel tensor specifying the physics of collision-coalescence" + kernel::KT + "a cloud droplet mass distribution function" + dist::D + "the moments of `dist` that the model should return" + moments::Array{FT, 1} + "time period over which to run the model, e.g., `(0, 1)`" + tspan::Tuple{FT, FT} +end + + +""" + run_dyn_model(ϕ::Array{FT, 1}, settings::ModelSettings{FT}) where {FT<:AbstractFloat} + +Run the dynamical model (Cloudy) for the given parameter vector ϕ. +Return the model output, a vector of moments of the particle mass +distribution at the end time of the simulation. + + - `ϕ` - parameter vector of length N_parameters + - `settings` - a ModelSettings struct + +""" +function run_dyn_model(ϕ::Array{FT, 1}, settings::ModelSettings{FT}) where {FT <: AbstractFloat} + + # Generate the initial distribution + # TODO: Obviously the GammaPrimitiveParticleDistribution should not be + # hard-coded here. Since update_params has been removed from + # ParticleDistributions.jl, I tried the following: + # Determine the type of the distribution, then create a new instance of + # that type using the desired parameters. This doesn't work; I get an + # error saying LoadError: MethodError: no method matching GammaPrimitiveParticleDistribution{Float64}(::Float64, ::Float64, ::Float64) + + #dist_init_type = typeof(settings.dist) + #dist_init = dist_init_type(ϕ...) + dist_init = GammaPrimitiveParticleDistribution(ϕ...) + moments_init = get_moments(dist_init) + #dist_init = settings.dist(ϕ...) + + +# ################ below is the "original" setup" +# # Numerical parameters + tol = FT(1e-7) +# +# # Set up ODE problem: dM/dt = f(M, ϕ, t) +# rhs(M, par, t) = get_int_coalescence(M, par, settings.kernel) +# ODE_par = Dict(:dist => dist_init) # ODE parameters +# prob = ODEProblem(rhs, moments_init, settings.tspan, ODE_par) +# # Solve the ODE +# sol = solve(prob, CVODE_BDF(), alg_hints = [:stiff], reltol = tol, abstol = tol) +# # +# ################ above is the "original" setup + + + ################ below is the new setup (with unreleased Cloudy code) + # Set up ODE problem: dM/dt = f(M, ϕ, t) + tspan = (FT(0), FT(1)) + #kernel_func = x -> 5e-3 * (x[1] + x[2]) + coalescence_coeff = 1 / 3.14 / 4 / 100 + kernel_func = x -> coalescence_coeff + kernel = CoalescenceTensor(kernel_func, 0, FT(100)) + ODE_parameters = Dict( + :dist => [dist_init], + :kernel => settings.kernel, + :dt => FT(1) + ) + #rhs = make_box_model_rhs(OneModeCoalStyle()) + rhs(m, par, t) = get_int_coalescence(OneModeCoalStyle(), m, par, par[:kernel]) + prob = ODEProblem(rhs, moments_init, settings.tspan, ODE_parameters) + #sol = solve(prob, SSPRK33(), dt = ODE_parameters[:dt]) + sol = solve(prob, CVODE_BDF(), alg_hints = [:stiff], reltol = tol, abstol = tol) + # + ################ above is the new setup + + # Return moments at last time step + moments_final = vcat(sol.u'...)[end, :] + + return moments_final +end + +""" + make_box_model_rhs(coal_type::CoalescenceStyle) + + `coal_type` type of coal source term function: OneModeCoalStyle, TwoModesCoalStyle, NumericalCoalStyle +Returns a function representing the right hand side of the ODE equation containing divergence +of coalescence source term. +""" +# TODO: update the analytical coalescence style to NOT re-allocate matrices +function make_box_model_rhs(coal_type::AnalyticalCoalStyle) + rhs(m, par, t) = get_int_coalescence(coal_type, m, par, par[:kernel]) +end + +end # module diff --git a/examples/deprecated/Cloudy/GModel.jl b/examples/deprecated/Cloudy/GModel.jl deleted file mode 100644 index c932671f8..000000000 --- a/examples/deprecated/Cloudy/GModel.jl +++ /dev/null @@ -1,116 +0,0 @@ -module GModel - -using DocStringExtensions - -# TODO: Remove build (which currently prevents segfault): -using Pkg -Pkg.build() - -using Random -using Distributions -using LinearAlgebra - -using DifferentialEquations -using Sundials # CVODE_BDF() solver for ODE - -export run_G -export run_G_ensemble - -# TODO: It would be nice to have run_G_ensemble take a pointer to the -# function G (called run_G below), which maps the parameters u to G(u), -# as an input argument. In the example below, run_G runs the model, but -# in general run_G will be supplied by the user and run the specific -# model the user wants to do UQ with. -# So, the interface would ideally be something like: -# run_G_ensemble(params, G) where G is user-defined -""" -$(DocStringExtensions.TYPEDEF) - -Structure to hold all information to run the forward model *G*. - -# Fields -$(DocStringExtensions.TYPEDFIELDS) -""" -struct GSettings{FT <: AbstractFloat, KT, D} - "A kernel tensor." - kernel::KT - "A model distribution." - dist::D - "The moments of `dist` that model should return." - moments::Array{FT, 1} - "Time period over which to run the model, e.g., `(0, 1)`." - tspan::Tuple{FT, FT} -end - - -""" -$(DocStringExtensions.TYPEDSIGNATURES) - -Run the forward model *G* for an array of parameters by iteratively -calling `run_G` for each of the *N\\_ensemble* parameter values. - -- `params` - array of size (*N\\_ensemble* × *N\\_parameters*) containing the parameters for which - G will be run. -- `settings` - a [GSetttings](@ref) struct. - -Returns `g_ens``, an array of size (*N\\_ensemble* × *N\\_data*), where g_ens[j,:] = G(params[j,:]). -""" -function run_G_ensemble( - params::Array{FT, 2}, - settings::GSettings{FT}, - update_params, - moment, - get_src; - rng_seed = 42, -) where {FT <: AbstractFloat} - - N_ens = size(params, 2) # params is N_ens x N_params - n_moments = length(settings.moments) - g_ens = zeros(n_moments, N_ens) - - Random.seed!(rng_seed) - for i in 1:N_ens - # run the model with the current parameters, i.e., map θ to G(θ) - g_ens[:, i] = run_G(params[:, i], settings, update_params, moment, get_src) - end - - return g_ens -end - - -""" -$(DocStringExtensions.TYPEDSIGNATURES) - -- `u` - parameter vector of length *N\\_parameters*. -- `settings` - a [GSetttings](@ref) struct. - -Returns `g_u` = *G(u)*, a vector of length *N\\_data*. -""" -function run_G(u::Array{FT, 1}, settings::GSettings{FT}, update_params, moment, get_src) where {FT <: AbstractFloat} - - # generate the initial distribution - dist = update_params(settings.dist, u) - - # Numerical parameters - tol = FT(1e-7) - - # Make sure moments are up to date. mom0 is the initial condition for the - # ODE problem - moments = settings.moments - moments_init = fill(NaN, length(moments)) - for (i, mom) in enumerate(moments) - moments_init[i] = moment(dist, convert(FT, mom)) - end - - # Set up ODE problem: dM/dt = f(M,p,t) - rhs(M, p, t) = get_src(M, dist, settings.kernel) - prob = ODEProblem(rhs, moments_init, settings.tspan) - # Solve the ODE - sol = solve(prob, CVODE_BDF(), alg_hints = [:stiff], reltol = tol, abstol = tol) - # Return moments at last time step - moments_final = vcat(sol.u'...)[end, :] - - return moments_final -end - -end # module diff --git a/examples/deprecated/Cloudy/Project.toml b/examples/deprecated/Cloudy/Project.toml index 7dc639a81..f48810fef 100644 --- a/examples/deprecated/Cloudy/Project.toml +++ b/examples/deprecated/Cloudy/Project.toml @@ -12,7 +12,6 @@ Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd" -Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4" [compat] julia = "~1.6" From 2bc028a60491d413f4ead69d85abd29be265b4aa Mon Sep 17 00:00:00 2001 From: Melanie Date: Mon, 13 Nov 2023 15:36:42 -0500 Subject: [PATCH 02/15] Save progress: add first working version with RF emulator (still very ugly though) --- examples/deprecated/Cloudy/Cloudy_example.jl | 51 ++-- .../Cloudy/Cloudy_example_with_RF_emulator.jl | 243 ++++++++++++++++++ 2 files changed, 276 insertions(+), 18 deletions(-) create mode 100644 examples/deprecated/Cloudy/Cloudy_example_with_RF_emulator.jl diff --git a/examples/deprecated/Cloudy/Cloudy_example.jl b/examples/deprecated/Cloudy/Cloudy_example.jl index b1b901084..5f5d04b28 100644 --- a/examples/deprecated/Cloudy/Cloudy_example.jl +++ b/examples/deprecated/Cloudy/Cloudy_example.jl @@ -93,14 +93,12 @@ end # Define the parameters that we want to learn # We assume that the true particle mass distribution is a Gamma # distribution with parameters N0_true, θ_true, k_true -par_names = ["N0", "θ", "k"] -n_par = length(par_names) +param_names = ["N0", "θ", "k"] +n_params = length(param_names) N0_true = 300.0 # number of particles (scaling factor for Gamma distribution) θ_true = 1.5597 # scale parameter of Gamma distribution k_true = 0.0817 # shape parameter of Gamma distribution -# Note that dist_true is a Cloudy distribution, not a Distributions.jl -# distribution -ϕ_true = [N0_true, θ_true, k_true] +ϕ_true = [N0_true, θ_true, k_true] # true parameters in constrained space dist_true = ParticleDistributions.GammaPrimitiveParticleDistribution(ϕ_true...) @@ -160,7 +158,7 @@ for i in 1:n_samples end truth = Observations.Observation(y_t, Γy, data_names) -truth_sample = truth.mean +truth_sample = truth.mean # TODO: should this be yt[:, end] ### @@ -169,10 +167,10 @@ truth_sample = truth.mean N_ens = 50 # number of ensemble members N_iter = 8 # number of EKI iterations -# initial parameters: N_par x N_ens -initial_par = construct_initial_ensemble(rng, priors, N_ens) +# initial parameters: n_params x N_ens +initial_params = construct_initial_ensemble(rng, priors, N_ens) ekiobj = EnsembleKalmanProcess( - initial_par, + initial_params, truth_sample, truth.obs_noise_cov, Inversion(), @@ -180,7 +178,7 @@ ekiobj = EnsembleKalmanProcess( # Initialize a ParticleDistribution with dummy parameters. The parameters # will then be set within `run_dyn_model` -dummy = ones(n_par) +dummy = ones(n_params) dist_type = ParticleDistributions.GammaPrimitiveParticleDistribution(dummy...) model_settings = DynamicalModel.ModelSettings(kernel, dist_type, moments, tspan) # EKI iterations @@ -203,8 +201,25 @@ println(get_u_mean_final(ekiobj)) u_stored = get_u(ekiobj, return_array = false) g_stored = get_g(ekiobj, return_array = false) -@save data_save_directory * "parameter_storage_eki.jld2" u_stored -@save data_save_directory * "data_storage_eki.jld2" g_stored +#@save data_save_directory * "parameter_storage_eki.jld2" u_stored +#@save data_save_directory * "data_storage_eki.jld2" g_stored +save( + joinpath(data_save_directory, "cloudy_calibrate_results.jld2"), + "inputs", + u_stored, + "outputs", + g_stored, + "priors", + priors, + "eki", + ekiobj, + "truth_sample", + truth_sample, + "truth_sample_mean", + truth.mean, + "truth_input_constrained", + ϕ_true, #constrained here, as these are in a physically constrained space (unlike the u inputs), +) #plots - unconstrained gr(size = (1200, 400)) @@ -327,7 +342,7 @@ pred_type = Emulators.YType() gp_kernel = SE(1.0, 1.0) + Mat52Ard(zeros(3), 0.0) + Noise(log(2.0)) gauss_proc = GaussianProcess( gppackage; - kernel = gp_kernel, g use default squared exponential kernel + kernel = gp_kernel, prediction_type = pred_type, noise_learn = false, ) @@ -388,8 +403,8 @@ for idx in 1:n_params throw("not implemented") end - label = "true " * par_names[idx] - posterior_samples = dropdims(get_distribution(posterior)[par_names[idx]], dims = 1) + label = "true " * param_names[idx] + posterior_samples = dropdims(get_distribution(posterior)[param_names[idx]], dims = 1) histogram( posterior_samples, bins = 100, @@ -399,11 +414,11 @@ for idx in 1:n_params lab = "posterior", legend = :outertopright, ) - prior_dist = get_distribution(mcmc.prior)[par_names[idx]] + prior_dist = get_distribution(mcmc.prior)[param_names[idx]] plot!(xs, prior_dist, w = 2.6, color = :blue, lab = "prior") plot!([θ_true[idx]], seriestype = "vline", w = 2.6, lab = label) - title!(par_names[idx]) - figpath = joinpath(figure_save_directory, "posterior_" * par_names[idx] * ".png") + title!(param_names[idx]) + figpath = joinpath(figure_save_directory, "posterior_" * param_names[idx] * ".png") StatsPlots.savefig(figpath) linkfig(figpath) end diff --git a/examples/deprecated/Cloudy/Cloudy_example_with_RF_emulator.jl b/examples/deprecated/Cloudy/Cloudy_example_with_RF_emulator.jl new file mode 100644 index 000000000..546d6d465 --- /dev/null +++ b/examples/deprecated/Cloudy/Cloudy_example_with_RF_emulator.jl @@ -0,0 +1,243 @@ +# Reference the in-tree version of CalibrateEmulateSample on Julias load path +include(joinpath(@__DIR__, "../..", "ci", "linkfig.jl")) +include(joinpath(@__DIR__, "DynamicalModel.jl")) # Import the module that runs Cloudy + +# This example requires Cloudy to be installed (it's best to install the master +# branch), which can be done by: +#] add Cloudy#master +using Cloudy +using Cloudy.ParticleDistributions +using Cloudy.KernelTensors + +# Import the module that runs Cloudy +#include("DynamicalModel.jl") +#using .DynamicalModel + +# Import modules +using Distributions # probability distributions and associated functions +using StatsBase +#using StableRNGs # needed? +using LinearAlgebra +using StatsPlots +using Plots +using Plots.PlotMeasures # is this needed? +using Random +using JLD2 # is this needed? + +# Import Calibrate-Emulate-Sample modules +# For the calibration step we use the EnsembleKalmanProcesses package, and +# for the sampling we use Markov chain Monte Carlo methods. We'll +# run this example twice, using first a Gaussian process emulator, and +# then a Random Feature emulator. +using EnsembleKalmanProcesses +using EnsembleKalmanProcesses.Observations +using EnsembleKalmanProcesses.ParameterDistributions +using EnsembleKalmanProcesses.DataContainers +using CalibrateEmulateSample.Emulators +using CalibrateEmulateSample.MarkovChainMonteCarlo +using CalibrateEmulateSample.Utilities + +# This example requires Cloudy to be installed. +using Cloudy +const PDistributions = Cloudy.ParticleDistributions + +function get_standardizing_factors(data::Array{FT, 2}) where {FT} + # Input: data size: N_data x N_ensembles + # Ensemble median of the data + norm_factor = median(data, dims = 2) # N_data x 1 array + return norm_factor +end + + +################################################################################ +# # +# Cloudy Calibrate-Emulate-Sample Example # +# # +# # +# This example uses Cloudy, a microphysics model that simulates the # +# coalescence of cloud droplets into bigger drops, to demonstrate how # +# the full Calibrate-Emulate-Sample pipeline can be used for Bayesian # +# learning and uncertainty quantification of parameters, given some # +# observations. # +# # +# Specifically, this examples shows how to learn parameters of the # +# initial cloud droplet mass distribution, given observations of some # +# moments of that mass distribution at a later time, after some of the # +# droplets have collided and become bigger drops. # +# # +# In this example, Cloudy is used in a "perfect model" (aka "known # +# truth") setting, which means that the "observations" are generated by # +# Cloudy itself, by running it with the true parameter values. In more # +# realistic applications, the observations will come from some external # +# measurement system. # +# # +# The purpose is to show how to do parameter learning using # +# Calibrate-Emulate-Sample in a simple (and highly artificial) setting. # +# # +# For more information on Cloudy, see # +# https://github.com/CliMA/Cloudy.jl.git # +# # +################################################################################ + + +rng_seed = 41 +Random.seed!(rng_seed) +rng = Random.seed!(Random.GLOBAL_RNG, rng_seed) + +homedir = pwd() +figure_save_directory = homedir * "/output/" +data_save_directory = homedir * "/output/" + +data_save_file = joinpath(data_save_directory, "cloudy_calibrate_results.jld2") +ekiobj = load(data_save_file)["eki"] +priors = load(data_save_file)["priors"] +truth_sample_mean = load(data_save_file)["truth_sample_mean"] +truth_sample = load(data_save_file)["truth_sample"] +# True parameters: +# - ϕ: in constrained space +# - θ: in unconstrained space +ϕ_true = load(data_save_file)["truth_input_constrained"] +θ_true = transform_constrained_to_unconstrained(priors, ϕ_true) +Γy = ekiobj.obs_noise_cov + +n_params = length(ϕ_true) # input dimension + + +### +### Emulate: Random Features +### + + +# Setup random features +n_features = 400 + +min_iter = 1 +max_iter = 5 # number of EKP iterations to use data from is at most this +optimizer_options = Dict( + "verbose" => true, + "scheduler" => DataMisfitController(terminate_at = 100.0), + "cov_sample_multiplier" => 1.0, + "n_iteration" => 20, +) + +nugget = 1e-8 # What is this? +kernel_structure = SeparableKernel(LowRankFactor(3, nugget), OneDimFactor()) +srfi = ScalarRandomFeatureInterface( + n_features, + n_par, + kernel_structure = kernel_structure, + optimizer_options = optimizer_options, +) + +## Standardize the output data +#input_output_pairs = Utilities.get_training_points(ekiobj, N_iter) +norm_factor = get_standardizing_factors(get_outputs(input_output_pairs)) +norm_factor = vcat(norm_factor...) + +# Get training points from the EKP iteration number in the second input term +N_iter = min(max_iter, length(get_u(ekiobj)) - 1) # number of paired iterations taken from EKP +min_iter = min(max_iter, max(1, min_iter)) +input_output_pairs = Utilities.get_training_points(ekiobj, min_iter:(N_iter - 1)) +input_output_pairs_test = Utilities.get_training_points(ekiobj, N_iter:(length(get_u(ekiobj)) - 1)) # "next" iterations +# Save data +@save joinpath(data_save_directory, "cloudy_input_output_pairs.jld2") input_output_pairs + +# Train emulator +standardize = true +retained_svd_frac = 1.0 +normalized = true +# do we want to use SVD to decorrelate outputs +decorrelate = true + + +emulator = Emulator( + srfi, + input_output_pairs; + obs_noise_cov = Γy, + normalize_inputs = normalized, + standardize_outputs = standardize, + standardize_outputs_factors = norm_factor, + retained_svd_frac = retained_svd_frac, + decorrelate = decorrelate, +) + +optimize_hyperparameters!(emulator) + +# Check how well the Random Feature emulator predicts on the +# true parameters +y_mean, y_var = Emulators.predict(emulator, reshape(θ_true, :, 1); transform_to_real = true) + +y_mean_test, y_var_test = + Emulators.predict(emulator, get_inputs(input_output_pairs_test), transform_to_real = true) + +println("Random Feature (RF) emulator prediction on true parameters: ") +println(vec(y_mean)) +println("true data: ") +println(truth_sample) # what was used as truth +println("RF predicted standard deviation") +println(sqrt.(diag(y_var[1], 0))) +println("RF MSE (truth): ") +println(mean((truth_sample - vec(y_mean)) .^ 2)) +println("RF MSE (next ensemble): ") +println(mean((get_outputs(input_output_pairs_test) - y_mean_test) .^ 2)) + +### +### Sample: Markov Chain Monte Carlo +### + +# initial values +u0 = vec(mean(get_inputs(input_output_pairs), dims = 2)) +println("initial parameters: ", u0) + +# First let's run a short chain to determine a good step size +yt_sample = truth_sample +mcmc = MCMCWrapper(RWMHSampling(), yt_sample, priors, emulator; init_params = u0) +new_step = optimize_stepsize(mcmc; init_stepsize = 0.1, N = 2000, discard_initial = 0) + +# Now begin the actual MCMC +println("Begin MCMC - with step size ", new_step) +chain = MarkovChainMonteCarlo.sample(mcmc, 100_000; stepsize = new_step, discard_initial = 1_000) +posterior = MarkovChainMonteCarlo.get_posterior(mcmc, chain) + +post_mean = mean(posterior) +post_cov = cov(posterior) +println("posterior mean") +println(post_mean) +println("posterior covariance") +println(post_cov) + +# Plot the posteriors together with the priors and the true parameter values +# (in the transformed/unconstrained space) + +gr(size = (800, 600)) + +for idx in 1:n_params + if idx == 1 + xs = collect(range(3.0, stop = 5.0, length = 1000)) + elseif idx == 2 + xs = collect(range(0.0, stop = 0.5, length = 1000)) + elseif idx == 3 + xs = collect(range(-3.0, stop = -2.0, length = 1000)) + else + throw("not implemented") + end + + label = "true " * par_names[idx] + posterior_samples = dropdims(get_distribution(posterior)[par_names[idx]], dims = 1) + histogram( + posterior_samples, + bins = 100, + normed = true, + fill = :slategray, + thickness_scaling = 2.0, + lab = "posterior", + legend = :outertopright, + ) + prior_dist = get_distribution(mcmc.prior)[par_names[idx]] + plot!(xs, prior_dist, w = 2.6, color = :blue, lab = "prior") + plot!([θ_true[idx]], seriestype = "vline", w = 2.6, lab = label) + title!(par_names[idx]) + figpath = joinpath(figure_save_directory, "posterior_" * par_names[idx] * "_RF_emulator.png") + StatsPlots.savefig(figpath) + linkfig(figpath) +end From a029bffb8766440d389c2f2436a6e7a3d9ef0667 Mon Sep 17 00:00:00 2001 From: Melanie Date: Fri, 24 Nov 2023 16:49:05 -0500 Subject: [PATCH 03/15] Separate Cloudy example into a "calibrate" file and "emulate + sample" file --- ...{Cloudy_example.jl => Cloudy_calibrate.jl} | 177 +++------- .../Cloudy/Cloudy_emulate_sample.jl | 312 ++++++++++++++++++ .../Cloudy/Cloudy_example_with_RF_emulator.jl | 243 -------------- examples/deprecated/Cloudy/Manifest.toml | 43 ++- 4 files changed, 396 insertions(+), 379 deletions(-) rename examples/deprecated/Cloudy/{Cloudy_example.jl => Cloudy_calibrate.jl} (66%) create mode 100644 examples/deprecated/Cloudy/Cloudy_emulate_sample.jl delete mode 100644 examples/deprecated/Cloudy/Cloudy_example_with_RF_emulator.jl diff --git a/examples/deprecated/Cloudy/Cloudy_example.jl b/examples/deprecated/Cloudy/Cloudy_calibrate.jl similarity index 66% rename from examples/deprecated/Cloudy/Cloudy_example.jl rename to examples/deprecated/Cloudy/Cloudy_calibrate.jl index 5f5d04b28..47d4c3a46 100644 --- a/examples/deprecated/Cloudy/Cloudy_example.jl +++ b/examples/deprecated/Cloudy/Cloudy_calibrate.jl @@ -1,6 +1,7 @@ # Reference the in-tree version of CalibrateEmulateSample on Julias load path include(joinpath(@__DIR__, "../..", "ci", "linkfig.jl")) -include(joinpath(@__DIR__, "DynamicalModel.jl")) # Import the module that runs Cloudy +# Import the module that runs Cloudy +include(joinpath(@__DIR__, "DynamicalModel.jl")) # This example requires Cloudy to be installed (it's best to install the master # branch), which can be done by: @@ -8,38 +9,25 @@ include(joinpath(@__DIR__, "DynamicalModel.jl")) # Import the module that runs C using Cloudy using Cloudy.ParticleDistributions using Cloudy.KernelTensors - -# Import the module that runs Cloudy -#include("DynamicalModel.jl") -#using .DynamicalModel +using Cloudy +const PDistributions = Cloudy.ParticleDistributions # Import modules using Distributions # probability distributions and associated functions using StatsBase -using GaussianProcesses using LinearAlgebra using StatsPlots using Plots -using Plots.PlotMeasures # is this needed? +#using Plots.PlotMeasures # is this needed? using Random using JLD2 # is this needed? -# Import Calibrate-Emulate-Sample modules -# For the calibration step we use the EnsembleKalmanProcesses package, and -# for the sampling we use Markov chain Monte Carlo methods. We'll -# run this example twice, using first a Gaussian process emulator, and -# then a Random Feature emulator. +# Import Ensemble Kalman Processes modules using EnsembleKalmanProcesses using EnsembleKalmanProcesses.Observations using EnsembleKalmanProcesses.ParameterDistributions using EnsembleKalmanProcesses.DataContainers -using CalibrateEmulateSample.Emulators -using CalibrateEmulateSample.MarkovChainMonteCarlo -using CalibrateEmulateSample.Utilities -# This example requires Cloudy to be installed. -using Cloudy -const PDistributions = Cloudy.ParticleDistributions ################################################################################ # # @@ -108,11 +96,12 @@ dist_true = ParticleDistributions.GammaPrimitiveParticleDistribution(ϕ_true...) # We choose to use normal distributions to represent the prior distributions of # the parameters in the transformed (unconstrained) space. i.e log coordinates -prior_N0 = constrained_gaussian(par_names[1], 400, 300, 0.4 * N0_true, Inf) -prior_θ = constrained_gaussian(par_names[2], 1.0, 5.0, 1e-1, Inf) -prior_k = constrained_gaussian(par_names[3], 0.2, 1.0, 1e-4, Inf) +prior_N0 = constrained_gaussian(param_names[1], 400, 300, 0.4 * N0_true, Inf) +prior_θ = constrained_gaussian(param_names[2], 1.0, 5.0, 1e-1, Inf) +prior_k = constrained_gaussian(param_names[3], 0.2, 1.0, 1e-4, Inf) priors = combine_distributions([prior_N0, prior_θ, prior_k]) + ### ### Define the data from which we want to learn the parameters ### @@ -138,7 +127,8 @@ kernel = Cloudy.KernelTensors.CoalescenceTensor(kernel_func, 0, 300.0) ### Generate (artificial) truth samples ### -dyn_model_settings_true = DynamicalModel.ModelSettings(kernel, dist_true, moments, tspan) +dyn_model_settings_true = DynamicalModel.ModelSettings( + kernel, dist_true, moments, tspan) G_t = DynamicalModel.run_dyn_model(ϕ_true, dyn_model_settings_true) n_samples = 100 @@ -218,10 +208,10 @@ save( "truth_sample_mean", truth.mean, "truth_input_constrained", - ϕ_true, #constrained here, as these are in a physically constrained space (unlike the u inputs), + ϕ_true, ) -#plots - unconstrained +# Plots in the unconstrained space gr(size = (1200, 400)) u_init = get_u_prior(ekiobj) @@ -241,9 +231,11 @@ anim_eki_unconst_cloudy = @animate for i in 1:N_iter margin = 5mm, title = "EKI iteration = " * string(i), ) - plot!(p1, [θ_true[2]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") + plot!(p1, [θ_true[2]], seriestype = "hline", linestyle = :dash, + linecolor = :red, label = "optimum") - p2 = plot(u_i[2, :], u_i[3, :], seriestype = :scatter, xlims = extrema(u_init[2, :]), ylims = extrema(u_init[3, :])) + p2 = plot(u_i[2, :], u_i[3, :], seriestype = :scatter, + xlims = extrema(u_init[2, :]), ylims = extrema(u_init[3, :])) plot!( p2, [θ_true[2]], @@ -256,9 +248,12 @@ anim_eki_unconst_cloudy = @animate for i in 1:N_iter margin = 5mm, title = "EKI iteration = " * string(i), ) - plot!(p2, [θ_true[3]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") - p3 = plot(u_i[3, :], u_i[1, :], seriestype = :scatter, xlims = extrema(u_init[3, :]), ylims = extrema(u_init[1, :])) + plot!(p2, [θ_true[3]], seriestype = "hline", linestyle = :dash, + linecolor = :red, label = "optimum") + + p3 = plot(u_i[3, :], u_i[1, :], seriestype = :scatter, + xlims = extrema(u_init[3, :]), ylims = extrema(u_init[1, :])) plot!( p3, [θ_true[3]], @@ -271,18 +266,23 @@ anim_eki_unconst_cloudy = @animate for i in 1:N_iter margin = 5mm, title = "EKI iteration = " * string(i), ) - plot!(p3, [θ_true[1]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") + + plot!(p3, [θ_true[1]], seriestype = "hline", linestyle = :dash, + linecolor = :red, label = "optimum") p = plot(p1, p2, p3, layout = (1, 3)) end -gif(anim_eki_unconst_cloudy, joinpath(figure_save_directory, "eki_unconst_cloudy.gif"), fps = 1) # hide -# plots - constrained +gif(anim_eki_unconst_cloudy, + joinpath(figure_save_directory, "eki_unconst_cloudy.gif"), fps = 1) # hide + +# Plots in the constrained space ϕ_init = transform_unconstrained_to_constrained(priors, u_init) anim_eki_cloudy = @animate for i in 1:N_iter ϕ_i = get_ϕ(priors, ekiobj, i) - p1 = plot(ϕ_i[1, :], ϕ_i[2, :], seriestype = :scatter, xlims = extrema(ϕ_init[1, :]), ylims = extrema(ϕ_init[2, :])) + p1 = plot(ϕ_i[1, :], ϕ_i[2, :], seriestype = :scatter, + xlims = extrema(ϕ_init[1, :]), ylims = extrema(ϕ_init[2, :])) plot!( p1, [ϕ_true[1]], @@ -295,9 +295,13 @@ anim_eki_cloudy = @animate for i in 1:N_iter label = false, title = "EKI iteration = " * string(i), ) - plot!(p1, [ϕ_true[2]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") - p2 = plot(ϕ_i[2, :], ϕ_i[3, :], seriestype = :scatter, xlims = extrema(ϕ_init[2, :]), ylims = extrema(ϕ_init[3, :])) + plot!(p1, [ϕ_true[2]], seriestype = "hline", linestyle = :dash, + linecolor = :red, label = "optimum") + + p2 = plot(ϕ_i[2, :], ϕ_i[3, :], seriestype = :scatter, + xlims = extrema(ϕ_init[2, :]), ylims = extrema(ϕ_init[3, :])) + plot!( p2, [ϕ_true[2]], @@ -310,9 +314,12 @@ anim_eki_cloudy = @animate for i in 1:N_iter label = false, title = "EKI iteration = " * string(i), ) - plot!(p2, [ϕ_true[3]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") - p3 = plot(ϕ_i[3, :], ϕ_i[1, :], seriestype = :scatter, xlims = extrema(ϕ_init[3, :]), ylims = extrema(ϕ_init[1, :])) + plot!(p2, [ϕ_true[3]], seriestype = "hline", linestyle = :dash, + linecolor = :red, label = "optimum") + + p3 = plot(ϕ_i[3, :], ϕ_i[1, :], seriestype = :scatter, + xlims = extrema(ϕ_init[3, :]), ylims = extrema(ϕ_init[1, :])) plot!( p3, [ϕ_true[3]], @@ -325,100 +332,12 @@ anim_eki_cloudy = @animate for i in 1:N_iter label = false, title = "EKI iteration = " * string(i), ) - plot!(p3, [ϕ_true[1]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") + plot!(p3, [ϕ_true[1]], seriestype = "hline", linestyle = :dash, + linecolor = :red, label = "optimum") p = plot(p1, p2, p3, layout = (1, 3)) -end -gif(anim_eki_cloudy, joinpath(figure_save_directory, "eki_cloudy.gif"), fps = 1) # hide - -### -### Emulate: Gaussian Process regression -### - - -gppackage = Emulators.GPJL() -pred_type = Emulators.YType() -gp_kernel = SE(1.0, 1.0) + Mat52Ard(zeros(3), 0.0) + Noise(log(2.0)) -gauss_proc = GaussianProcess( - gppackage; - kernel = gp_kernel, - prediction_type = pred_type, - noise_learn = false, -) - -# Get training points -input_output_pairs = Utilities.get_training_points(ekiobj, N_iter) -emulator = Emulator(gauss_proc, input_output_pairs, obs_noise_cov = Γy, normalize_inputs = true) -optimize_hyperparameters!(emulator) - -# Check how well the Gaussian Process regression predicts on the -# true parameters -y_mean, y_var = Emulators.predict(emulator, reshape(θ_true, :, 1); transform_to_real = true) -println("GP prediction on true parameters: ") -println(vec(y_mean)) -println("true data: ") -println(truth.mean) - - -### -### Sample: Markov Chain Monte Carlo -### - -# initial values -u0 = vec(mean(get_inputs(input_output_pairs), dims = 2)) -println("initial parameters: ", u0) - -# First let's run a short chain to determine a good step size -yt_sample = truth_sample -mcmc = MCMCWrapper(RWMHSampling(), yt_sample, priors, emulator; init_params = u0) -new_step = optimize_stepsize(mcmc; init_stepsize = 0.1, N = 2000, discard_initial = 0) - -# Now begin the actual MCMC -println("Begin MCMC - with step size ", new_step) -chain = MarkovChainMonteCarlo.sample(mcmc, 100_000; stepsize = new_step, discard_initial = 1_000) -posterior = MarkovChainMonteCarlo.get_posterior(mcmc, chain) - -post_mean = mean(posterior) -post_cov = cov(posterior) -println("posterior mean") -println(post_mean) -println("posterior covariance") -println(post_cov) - -# Plot the posteriors together with the priors and the true parameter values -# (in the transformed/unconstrained space) -n_params = length(get_name(posterior)) - -gr(size = (800, 600)) - -for idx in 1:n_params - if idx == 1 - xs = collect(range(5.15, stop = 5.25, length = 1000)) - elseif idx == 2 - xs = collect(range(0.0, stop = 0.5, length = 1000)) - elseif idx == 3 - xs = collect(range(-3.0, stop = -2.0, length = 1000)) - else - throw("not implemented") - end - - label = "true " * param_names[idx] - posterior_samples = dropdims(get_distribution(posterior)[param_names[idx]], dims = 1) - histogram( - posterior_samples, - bins = 100, - normed = true, - fill = :slategray, - thickness_scaling = 2.0, - lab = "posterior", - legend = :outertopright, - ) - prior_dist = get_distribution(mcmc.prior)[param_names[idx]] - plot!(xs, prior_dist, w = 2.6, color = :blue, lab = "prior") - plot!([θ_true[idx]], seriestype = "vline", w = 2.6, lab = label) - title!(param_names[idx]) - figpath = joinpath(figure_save_directory, "posterior_" * param_names[idx] * ".png") - StatsPlots.savefig(figpath) - linkfig(figpath) end + +gif(anim_eki_cloudy, + joinpath(figure_save_directory, "eki_cloudy.gif"), fps = 1) # hide diff --git a/examples/deprecated/Cloudy/Cloudy_emulate_sample.jl b/examples/deprecated/Cloudy/Cloudy_emulate_sample.jl new file mode 100644 index 000000000..23897e40e --- /dev/null +++ b/examples/deprecated/Cloudy/Cloudy_emulate_sample.jl @@ -0,0 +1,312 @@ +# Reference the in-tree version of CalibrateEmulateSample on Julias load path +include(joinpath(@__DIR__, "../..", "ci", "linkfig.jl")) + +# Import modules +using Distributions # probability distributions and associated functions +using StatsBase +using GaussianProcesses +using LinearAlgebra +using StatsPlots +using Plots +using Plots.PlotMeasures # is this needed? +using Random +using JLD2 # is this needed? + +# Import Calibrate-Emulate-Sample modules +#using EnsembleKalmanProcesses.DataContainers +using EnsembleKalmanProcesses +using EnsembleKalmanProcesses.ParameterDistributions +using EnsembleKalmanProcesses.DataContainers +using CalibrateEmulateSample.Emulators +using CalibrateEmulateSample.MarkovChainMonteCarlo +using CalibrateEmulateSample.Utilities + +function get_standardizing_factors(data::Array{FT, 2}) where {FT} + # Input: data size: N_data x N_ensembles + # Ensemble median of the data + norm_factor = median(data, dims = 2) # N_data x 1 array + return norm_factor +end + +################################################################################ +# # +# Cloudy Calibrate-Emulate-Sample Example # +# # +# # +# This example uses Cloudy, a microphysics model that simulates the # +# coalescence of cloud droplets into bigger drops, to demonstrate how # +# the full Calibrate-Emulate-Sample pipeline can be used for Bayesian # +# learning and uncertainty quantification of parameters, given some # +# observations. # +# # +# Specifically, this examples shows how to learn parameters of the # +# initial cloud droplet mass distribution, given observations of some # +# moments of that mass distribution at a later time, after some of the # +# droplets have collided and become bigger drops. # +# # +# In this example, Cloudy is used in a "perfect model" (aka "known # +# truth") setting, which means that the "observations" are generated by # +# Cloudy itself, by running it with the true parameter values. In more # +# realistic applications, the observations will come from some external # +# measurement system. # +# # +# The purpose is to show how to do parameter learning using # +# Calibrate-Emulate-Sample in a simple (and highly artificial) setting. # +# # +# For more information on Cloudy, see # +# https://github.com/CliMA/Cloudy.jl.git # +# # +################################################################################ + + +function main() + + rng_seed = 41 + Random.seed!(rng_seed) + rng = Random.seed!(Random.GLOBAL_RNG, rng_seed) + + output_directory = joinpath(@__DIR__, "output") + if !isdir(output_directory) + mkdir(output_directory) + end + + # The calibration results must be produced by running Cloudy_calibrate.jl + # before running Cloudy_emulate_sample.jl + data_save_file = joinpath( + output_directory, + "cloudy_calibrate_results.jld2" + ) + + # Check if the file exists before loading + if isfile(data_save_file) + + ekiobj = load(data_save_file)["eki"] + priors = load(data_save_file)["priors"] + truth_sample_mean = load(data_save_file)["truth_sample_mean"] + truth_sample = load(data_save_file)["truth_sample"] + # True parameters: + # - ϕ: in constrained space + # - θ: in unconstrained space + ϕ_true = load(data_save_file)["truth_input_constrained"] + + else + error("File not found: $data_save_file. Please run 'Cloudy_calibrate.jl' first.") + + end + + θ_true = transform_constrained_to_unconstrained(priors, ϕ_true) + param_names = get_name(priors) + Γy = ekiobj.obs_noise_cov + n_params = length(ϕ_true) # input dimension + # Save data + #@save joinpath(output_directory, "cloudy_input_output_pairs.jld2") input_output_pairs + + cases = [ + "rf-scalar", + "gp-gpjl" # Veeeery slow predictions + ] + + # These settings are the same for all Gaussian Process cases + pred_type = YType() + + # These settings are the same for all Random Feature cases + n_features = 400 + nugget = 1e-8 + optimizer_options = Dict( + "verbose" => true, + "scheduler" => DataMisfitController(terminate_at = 100.0), + "cov_sample_multiplier" => 1.0, + "n_iteration" => 20, + ) + + # Specify cases to run (e.g., case_mask = [2] only runs the second case) + case_mask = [1] + println("case mask: ") + println(case_mask) + println(cases[case_mask]) + + for case in cases[case_mask] + + println(" ") + println("*********************************\n") + @info "running case $case" + + if case == "gp-gpjl" + + @warn "gp-gpjl case is very slow at prediction" + gppackage = GPJL() + gp_kernel = SE(1.0, 1.0) + Mat52Ard(zeros(3), 0.0) + Noise(log(2.0)) + gaussian_process = GaussianProcess( + gppackage; + kernel = gp_kernel, + prediction_type = pred_type, + noise_learn = false, + ) + + input_output_pairs = get_training_points(ekiobj, length(get_u(ekiobj))-1) + emulator = Emulator( + gaussian_process, + input_output_pairs, + obs_noise_cov = Γy, + normalize_inputs = true + ) + + elseif case == "rf-scalar" + + kernel_structure = SeparableKernel( + LowRankFactor(n_params, nugget), + OneDimFactor() + ) + + srfi = ScalarRandomFeatureInterface( + n_features, + n_params, + kernel_structure = kernel_structure, + optimizer_options = optimizer_options, + ) + + retained_svd_frac = 1.0 + min_iter = 1 + max_iter = 5 # number of EKP iterations to use data from is at most this + @assert min_iter <= max_iter + @assert max_iter <= length(get_u(ekiobj)) - 1 + @assert min_iter >= 1 + N_iter = min(max_iter, length(get_u(ekiobj)) - 1) # number of paired iterations taken from EKP + # Get training points from the EKP iteration number in the second input term + min_iter = min(max_iter, max(1, min_iter)) + input_output_pairs = get_training_points(ekiobj, min_iter:(N_iter - 1)) + input_output_pairs_test = get_training_points( + ekiobj, N_iter:(length(get_u(ekiobj)) - 1)) # "next" iterations + norm_factors = get_standardizing_factors( + get_outputs(input_output_pairs) + ) + + emulator = Emulator( + srfi, + input_output_pairs; + obs_noise_cov = Γy, + normalize_inputs = true, + standardize_outputs = true, + standardize_outputs_factors = vcat(norm_factors...), + retained_svd_frac = retained_svd_frac, + decorrelate = true # use SVD to decorrelate outputs + ) + + else + error("Case $case is not implemented yet.") + + end + + optimize_hyperparameters!(emulator) + + # Check how well the emulator predicts on the true parameters + y_mean, y_var = Emulators.predict( + emulator, + reshape(θ_true, :, 1); + transform_to_real = true + ) + + # Check how well the emulator predicts on the test input pairs (whose + # corresponding output we know, as it was calculated during EKI) + y_mean_test, y_var_test = + Emulators.predict( + emulator, + get_inputs(input_output_pairs_test), + transform_to_real = true + ) + + println("Emulator ($(case)) prediction on true parameters: ") + println(vec(y_mean)) + println("true data: ") + println(truth_sample) # what was used as truth + println("Emulator ($(case)) predicted standard deviation") + println(sqrt.(diag(y_var[1], 0))) + println("Emulator ($(case)) MSE (truth): ") + println(mean((truth_sample - vec(y_mean)) .^ 2)) + #println("Emulator ($(case)) MSE (next ensemble): ") + #println(mean((get_outputs(input_output_pairs_test) - y_mean_test) .^ 2)) + + ### + ### Sample: Markov Chain Monte Carlo + ### + + # initial values + u0 = vec(mean(get_inputs(input_output_pairs), dims = 2)) + println("initial parameters: ", u0) + + # First let's run a short chain to determine a good step size + yt_sample = truth_sample + mcmc = MCMCWrapper( + RWMHSampling(), + yt_sample, + priors, + emulator; + init_params = u0 + ) + + new_step = optimize_stepsize( + mcmc; + init_stepsize = 0.1, + N = 2000, + discard_initial = 0 + ) + + # Now begin the actual MCMC + println("Begin MCMC - with step size ", new_step) + chain = MarkovChainMonteCarlo.sample( + mcmc, + 100_000; + stepsize = new_step, + discard_initial = 1_000 + ) + + posterior = MarkovChainMonteCarlo.get_posterior(mcmc, chain) + + post_mean = mean(posterior) + post_cov = cov(posterior) + println("posterior mean") + println(post_mean) + println("posterior covariance") + println(post_cov) + + # Plot the posteriors together with the priors and the true parameter + # values (in the transformed/unconstrained space) + n_params = length(get_name(posterior)) + + gr(size = (800, 600)) + + for idx in 1:n_params + posterior_samples = dropdims( + get_distribution(posterior)[param_names[idx]], dims = 1) + + # Find the range of the posterior samples + xmin = minimum(posterior_samples) + xmax = maximum(posterior_samples) + xs = collect(range(xmin, stop = xmax, length = 1000)) + + label = "true " * param_names[idx] + histogram( + posterior_samples, + bins = 100, + normed = true, + fill = :slategray, + thickness_scaling = 2.0, + lab = "posterior", + legend = :outertopright, + ) + + prior_dist = get_distribution(mcmc.prior)[param_names[idx]] + plot!(xs, prior_dist, w = 2.6, color = :blue, lab = "prior") + plot!([θ_true[idx]], seriestype = "vline", w = 2.6, lab = label) + title!(param_names[idx]) + figname = "posterior_" * case * "_" * param_names[idx] * ".png" + figpath = joinpath(output_directory, figname) + StatsPlots.savefig(figpath) + linkfig(figpath) + + end + end +end + + +main() diff --git a/examples/deprecated/Cloudy/Cloudy_example_with_RF_emulator.jl b/examples/deprecated/Cloudy/Cloudy_example_with_RF_emulator.jl deleted file mode 100644 index 546d6d465..000000000 --- a/examples/deprecated/Cloudy/Cloudy_example_with_RF_emulator.jl +++ /dev/null @@ -1,243 +0,0 @@ -# Reference the in-tree version of CalibrateEmulateSample on Julias load path -include(joinpath(@__DIR__, "../..", "ci", "linkfig.jl")) -include(joinpath(@__DIR__, "DynamicalModel.jl")) # Import the module that runs Cloudy - -# This example requires Cloudy to be installed (it's best to install the master -# branch), which can be done by: -#] add Cloudy#master -using Cloudy -using Cloudy.ParticleDistributions -using Cloudy.KernelTensors - -# Import the module that runs Cloudy -#include("DynamicalModel.jl") -#using .DynamicalModel - -# Import modules -using Distributions # probability distributions and associated functions -using StatsBase -#using StableRNGs # needed? -using LinearAlgebra -using StatsPlots -using Plots -using Plots.PlotMeasures # is this needed? -using Random -using JLD2 # is this needed? - -# Import Calibrate-Emulate-Sample modules -# For the calibration step we use the EnsembleKalmanProcesses package, and -# for the sampling we use Markov chain Monte Carlo methods. We'll -# run this example twice, using first a Gaussian process emulator, and -# then a Random Feature emulator. -using EnsembleKalmanProcesses -using EnsembleKalmanProcesses.Observations -using EnsembleKalmanProcesses.ParameterDistributions -using EnsembleKalmanProcesses.DataContainers -using CalibrateEmulateSample.Emulators -using CalibrateEmulateSample.MarkovChainMonteCarlo -using CalibrateEmulateSample.Utilities - -# This example requires Cloudy to be installed. -using Cloudy -const PDistributions = Cloudy.ParticleDistributions - -function get_standardizing_factors(data::Array{FT, 2}) where {FT} - # Input: data size: N_data x N_ensembles - # Ensemble median of the data - norm_factor = median(data, dims = 2) # N_data x 1 array - return norm_factor -end - - -################################################################################ -# # -# Cloudy Calibrate-Emulate-Sample Example # -# # -# # -# This example uses Cloudy, a microphysics model that simulates the # -# coalescence of cloud droplets into bigger drops, to demonstrate how # -# the full Calibrate-Emulate-Sample pipeline can be used for Bayesian # -# learning and uncertainty quantification of parameters, given some # -# observations. # -# # -# Specifically, this examples shows how to learn parameters of the # -# initial cloud droplet mass distribution, given observations of some # -# moments of that mass distribution at a later time, after some of the # -# droplets have collided and become bigger drops. # -# # -# In this example, Cloudy is used in a "perfect model" (aka "known # -# truth") setting, which means that the "observations" are generated by # -# Cloudy itself, by running it with the true parameter values. In more # -# realistic applications, the observations will come from some external # -# measurement system. # -# # -# The purpose is to show how to do parameter learning using # -# Calibrate-Emulate-Sample in a simple (and highly artificial) setting. # -# # -# For more information on Cloudy, see # -# https://github.com/CliMA/Cloudy.jl.git # -# # -################################################################################ - - -rng_seed = 41 -Random.seed!(rng_seed) -rng = Random.seed!(Random.GLOBAL_RNG, rng_seed) - -homedir = pwd() -figure_save_directory = homedir * "/output/" -data_save_directory = homedir * "/output/" - -data_save_file = joinpath(data_save_directory, "cloudy_calibrate_results.jld2") -ekiobj = load(data_save_file)["eki"] -priors = load(data_save_file)["priors"] -truth_sample_mean = load(data_save_file)["truth_sample_mean"] -truth_sample = load(data_save_file)["truth_sample"] -# True parameters: -# - ϕ: in constrained space -# - θ: in unconstrained space -ϕ_true = load(data_save_file)["truth_input_constrained"] -θ_true = transform_constrained_to_unconstrained(priors, ϕ_true) -Γy = ekiobj.obs_noise_cov - -n_params = length(ϕ_true) # input dimension - - -### -### Emulate: Random Features -### - - -# Setup random features -n_features = 400 - -min_iter = 1 -max_iter = 5 # number of EKP iterations to use data from is at most this -optimizer_options = Dict( - "verbose" => true, - "scheduler" => DataMisfitController(terminate_at = 100.0), - "cov_sample_multiplier" => 1.0, - "n_iteration" => 20, -) - -nugget = 1e-8 # What is this? -kernel_structure = SeparableKernel(LowRankFactor(3, nugget), OneDimFactor()) -srfi = ScalarRandomFeatureInterface( - n_features, - n_par, - kernel_structure = kernel_structure, - optimizer_options = optimizer_options, -) - -## Standardize the output data -#input_output_pairs = Utilities.get_training_points(ekiobj, N_iter) -norm_factor = get_standardizing_factors(get_outputs(input_output_pairs)) -norm_factor = vcat(norm_factor...) - -# Get training points from the EKP iteration number in the second input term -N_iter = min(max_iter, length(get_u(ekiobj)) - 1) # number of paired iterations taken from EKP -min_iter = min(max_iter, max(1, min_iter)) -input_output_pairs = Utilities.get_training_points(ekiobj, min_iter:(N_iter - 1)) -input_output_pairs_test = Utilities.get_training_points(ekiobj, N_iter:(length(get_u(ekiobj)) - 1)) # "next" iterations -# Save data -@save joinpath(data_save_directory, "cloudy_input_output_pairs.jld2") input_output_pairs - -# Train emulator -standardize = true -retained_svd_frac = 1.0 -normalized = true -# do we want to use SVD to decorrelate outputs -decorrelate = true - - -emulator = Emulator( - srfi, - input_output_pairs; - obs_noise_cov = Γy, - normalize_inputs = normalized, - standardize_outputs = standardize, - standardize_outputs_factors = norm_factor, - retained_svd_frac = retained_svd_frac, - decorrelate = decorrelate, -) - -optimize_hyperparameters!(emulator) - -# Check how well the Random Feature emulator predicts on the -# true parameters -y_mean, y_var = Emulators.predict(emulator, reshape(θ_true, :, 1); transform_to_real = true) - -y_mean_test, y_var_test = - Emulators.predict(emulator, get_inputs(input_output_pairs_test), transform_to_real = true) - -println("Random Feature (RF) emulator prediction on true parameters: ") -println(vec(y_mean)) -println("true data: ") -println(truth_sample) # what was used as truth -println("RF predicted standard deviation") -println(sqrt.(diag(y_var[1], 0))) -println("RF MSE (truth): ") -println(mean((truth_sample - vec(y_mean)) .^ 2)) -println("RF MSE (next ensemble): ") -println(mean((get_outputs(input_output_pairs_test) - y_mean_test) .^ 2)) - -### -### Sample: Markov Chain Monte Carlo -### - -# initial values -u0 = vec(mean(get_inputs(input_output_pairs), dims = 2)) -println("initial parameters: ", u0) - -# First let's run a short chain to determine a good step size -yt_sample = truth_sample -mcmc = MCMCWrapper(RWMHSampling(), yt_sample, priors, emulator; init_params = u0) -new_step = optimize_stepsize(mcmc; init_stepsize = 0.1, N = 2000, discard_initial = 0) - -# Now begin the actual MCMC -println("Begin MCMC - with step size ", new_step) -chain = MarkovChainMonteCarlo.sample(mcmc, 100_000; stepsize = new_step, discard_initial = 1_000) -posterior = MarkovChainMonteCarlo.get_posterior(mcmc, chain) - -post_mean = mean(posterior) -post_cov = cov(posterior) -println("posterior mean") -println(post_mean) -println("posterior covariance") -println(post_cov) - -# Plot the posteriors together with the priors and the true parameter values -# (in the transformed/unconstrained space) - -gr(size = (800, 600)) - -for idx in 1:n_params - if idx == 1 - xs = collect(range(3.0, stop = 5.0, length = 1000)) - elseif idx == 2 - xs = collect(range(0.0, stop = 0.5, length = 1000)) - elseif idx == 3 - xs = collect(range(-3.0, stop = -2.0, length = 1000)) - else - throw("not implemented") - end - - label = "true " * par_names[idx] - posterior_samples = dropdims(get_distribution(posterior)[par_names[idx]], dims = 1) - histogram( - posterior_samples, - bins = 100, - normed = true, - fill = :slategray, - thickness_scaling = 2.0, - lab = "posterior", - legend = :outertopright, - ) - prior_dist = get_distribution(mcmc.prior)[par_names[idx]] - plot!(xs, prior_dist, w = 2.6, color = :blue, lab = "prior") - plot!([θ_true[idx]], seriestype = "vline", w = 2.6, lab = label) - title!(par_names[idx]) - figpath = joinpath(figure_save_directory, "posterior_" * par_names[idx] * "_RF_emulator.png") - StatsPlots.savefig(figpath) - linkfig(figpath) -end diff --git a/examples/deprecated/Cloudy/Manifest.toml b/examples/deprecated/Cloudy/Manifest.toml index 46ec9e740..9ec1ec910 100644 --- a/examples/deprecated/Cloudy/Manifest.toml +++ b/examples/deprecated/Cloudy/Manifest.toml @@ -14,6 +14,7 @@ version = "3.3.3" [[ArgTools]] uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" +version = "1.1.1" [[ArnoldiMethod]] deps = ["LinearAlgebra", "Random", "StaticArrays"] @@ -105,7 +106,7 @@ uuid = "2a0fbf3d-bb9c-48f3-b0a9-814d99fd7ab9" version = "0.1.6" [[Cairo_jll]] -deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] +deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"] git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2" uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a" version = "1.16.1+1" @@ -195,6 +196,7 @@ version = "3.41.0" [[CompilerSupportLibraries_jll]] deps = ["Artifacts", "Libdl"] uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" +version = "1.0.5+0" [[Conda]] deps = ["Downloads", "JSON", "VersionParsing"] @@ -259,7 +261,9 @@ version = "5.32.4" [[DelimitedFiles]] deps = ["Mmap"] +git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae" uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab" +version = "1.9.1" [[DiffEqBase]] deps = ["ArrayInterface", "ChainRulesCore", "DataStructures", "DocStringExtensions", "FastBroadcast", "FunctionWrappers", "IterativeSolvers", "LabelledArrays", "LinearAlgebra", "Logging", "MuladdMacro", "NonlinearSolve", "Parameters", "Printf", "RecursiveArrayTools", "RecursiveFactorization", "Reexport", "Requires", "SciMLBase", "Setfield", "SparseArrays", "StaticArrays", "Statistics", "SuiteSparse", "ZygoteRules"] @@ -350,8 +354,9 @@ uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" version = "0.8.6" [[Downloads]] -deps = ["ArgTools", "LibCURL", "NetworkOptions"] +deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"] uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6" +version = "1.6.0" [[EarCut_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] @@ -424,6 +429,9 @@ git-tree-sha1 = "6ea5f7b4aecce0e3a14ca1da03f62f86148c8fa3" uuid = "442a2c76-b920-505d-bb47-c5924d526838" version = "0.4.5" +[[FileWatching]] +uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee" + [[FillArrays]] deps = ["LinearAlgebra", "Random", "SparseArrays"] git-tree-sha1 = "4863cbb7910079369e258dee4add9d06ead5063a" @@ -691,10 +699,12 @@ version = "0.1.4" [[LibCURL]] deps = ["LibCURL_jll", "MozillaCACerts_jll"] uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21" +version = "0.6.3" [[LibCURL_jll]] deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"] uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0" +version = "7.84.0+0" [[LibGit2]] deps = ["Base64", "NetworkOptions", "Printf", "SHA"] @@ -703,6 +713,7 @@ uuid = "76f85450-5226-5b5a-8eaa-529ad045b433" [[LibSSH2_jll]] deps = ["Artifacts", "Libdl", "MbedTLS_jll"] uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8" +version = "1.10.2+0" [[Libdl]] uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb" @@ -756,7 +767,7 @@ uuid = "d3d80556-e9d4-5f37-9878-2ab0fcc64255" version = "7.1.1" [[LinearAlgebra]] -deps = ["Libdl"] +deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"] uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" [[LogExpFunctions]] @@ -809,6 +820,7 @@ version = "1.0.3" [[MbedTLS_jll]] deps = ["Artifacts", "Libdl"] uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1" +version = "2.28.2+0" [[Measures]] git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f" @@ -832,6 +844,7 @@ version = "2.0.0" [[MozillaCACerts_jll]] uuid = "14a3606d-f60d-562e-9121-12d972cd8159" +version = "2022.10.11" [[MuladdMacro]] git-tree-sha1 = "c6190f9a7fc5d9d5915ab29f2134421b12d24a68" @@ -881,6 +894,7 @@ version = "0.4.9" [[NetworkOptions]] uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908" +version = "1.2.0" [[NonlinearSolve]] deps = ["ArrayInterface", "FiniteDiff", "ForwardDiff", "IterativeSolvers", "LinearAlgebra", "RecursiveArrayTools", "RecursiveFactorization", "Reexport", "SciMLBase", "Setfield", "StaticArrays", "UnPack"] @@ -908,6 +922,7 @@ version = "1.3.5+1" [[OpenBLAS_jll]] deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"] uuid = "4536629a-c528-5b80-bd46-f80d51c5b363" +version = "0.3.21+4" [[OpenSSL_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] @@ -975,8 +990,9 @@ uuid = "30392449-352a-5448-841d-b1acce4e97dc" version = "0.40.1+0" [[Pkg]] -deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"] +deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"] uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" +version = "1.9.2" [[PlotThemes]] deps = ["PlotUtils", "Requires", "Statistics"] @@ -1064,7 +1080,7 @@ deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"] uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb" [[Random]] -deps = ["Serialization"] +deps = ["SHA", "Serialization"] uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" [[Random123]] @@ -1140,6 +1156,7 @@ version = "0.3.0+0" [[SHA]] uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" +version = "0.7.0" [[SIMDDualNumbers]] deps = ["ForwardDiff", "IfElse", "SLEEFPirates", "VectorizationBase"] @@ -1217,7 +1234,7 @@ uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c" version = "1.0.1" [[SparseArrays]] -deps = ["LinearAlgebra", "Random"] +deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"] uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" [[SparseDiffTools]] @@ -1247,6 +1264,7 @@ version = "0.12.5" [[Statistics]] deps = ["LinearAlgebra", "SparseArrays"] uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" +version = "1.9.0" [[StatsAPI]] git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6" @@ -1300,8 +1318,9 @@ deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"] uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9" [[SuiteSparse_jll]] -deps = ["Artifacts", "Libdl", "OpenBLAS_jll"] +deps = ["Artifacts", "Libdl", "Pkg", "libblastrampoline_jll"] uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c" +version = "5.10.1+6" [[Sundials]] deps = ["CEnum", "DataStructures", "DiffEqBase", "Libdl", "LinearAlgebra", "Logging", "Reexport", "SparseArrays", "Sundials_jll"] @@ -1318,6 +1337,7 @@ version = "5.2.0+1" [[TOML]] deps = ["Dates"] uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76" +version = "1.0.3" [[TableOperations]] deps = ["SentinelArrays", "Tables", "Test"] @@ -1340,6 +1360,7 @@ version = "1.6.1" [[Tar]] deps = ["ArgTools", "SHA"] uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e" +version = "1.10.0" [[TaylorSeries]] deps = ["InteractiveUtils", "LinearAlgebra", "Markdown", "Requires", "SparseArrays"] @@ -1479,6 +1500,7 @@ version = "1.4.0+3" [[Zlib_jll]] deps = ["Libdl"] uuid = "83775a58-1f1d-513f-b197-d71354ab007a" +version = "1.2.13+0" [[ZygoteRules]] deps = ["MacroTools"] @@ -1492,6 +1514,11 @@ git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47" uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" version = "0.15.1+0" +[[libblastrampoline_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" +version = "5.8.0+0" + [[libfdk_aac_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55" @@ -1513,10 +1540,12 @@ version = "1.3.7+0" [[nghttp2_jll]] deps = ["Artifacts", "Libdl"] uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" +version = "1.48.0+0" [[p7zip_jll]] deps = ["Artifacts", "Libdl"] uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" +version = "17.4.0+0" [[x264_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] From 6ce6e95136b15d70743554f888031fa70bba95a2 Mon Sep 17 00:00:00 2001 From: Melanie Date: Sun, 26 Nov 2023 18:51:17 -0500 Subject: [PATCH 04/15] Clean up Cloudy example and add first draft of documentation --- docs/src/examples/Cloudy_example.md | 510 ++++++++++++++++++ .../deprecated/Cloudy/Cloudy_calibrate.jl | 33 +- .../Cloudy/Cloudy_emulate_sample.jl | 71 +-- examples/deprecated/Cloudy/DynamicalModel.jl | 44 +- 4 files changed, 557 insertions(+), 101 deletions(-) create mode 100755 docs/src/examples/Cloudy_example.md diff --git a/docs/src/examples/Cloudy_example.md b/docs/src/examples/Cloudy_example.md new file mode 100755 index 000000000..6eea151dc --- /dev/null +++ b/docs/src/examples/Cloudy_example.md @@ -0,0 +1,510 @@ +# [Learning the initial parameters of a droplet mass distribution in Cloudy](@id Cloudy-example) + + +This example is based on [Cloudy](https://github.com/CliMA/Cloudy.jl.git), a +microphysics model that simulates how cloud droplets collide and coalesce into +larger drops. Collision-coalescence is a crucial process for the formation of +rain. + +Cloudy is initialized with a mass distribution of the cloud droplets; this +distribution is then stepped forward in time, with more and more droplets +colliding and combining into bigger drops according to the droplet-droplet +interactions specified by a collision-coalescence kernel. The evolution of the +droplet distribution is completely determined by the shape of the initial distribution and the form of the kernel. + +We will show how Calibrate-Emulate-Sample can be used to learn the parameters of +the initial cloud droplet mass distribution from observations of the moments of +that mass distribution at a later time. + +Cloudy is used here in a "perfect model" (aka "known truth") setting, which +means that the "observations" are generated by Cloudy itself, by running it with +the true parameter values---in more realistic applications, one would use actual measurements of cloud properties. + +[This paper](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022MS002994) describes Cloudy in much more detail and shows results of experiments using +Calibrate-Emulate-Sample to learn model parameters. + + +### Prerequisites + +In order to run this example, you need to install `Cloudy.jl`. The example was +written using Cloudy v0.3.0, which you can install as follows: +``` +pkg > add https://github.com/CliMA/Cloudy.jl.git#v0.3.0 +``` + +### Running the example + +`Cloudy_calibrate.jl` performs the calibration using ensemble Kalman +inversion; `Cloudy_emulate_sample.jl` fits an emulator and uses it to sample the +posterior distributions of the parameters. +Once Cloudy is installed, the example can be run from the julia REPL: +```julia +# +include("Cloudy_calibrate.jl") +include("Cloudy_emulate_sample.jl") +``` + +### Walkthrough of the code: `Cloudy_calibrate.jl` + + +#### Import packagages and modules + +First we load standard packages, + +```julia +using Distributions +using StatsBase +using LinearAlgebra +using StatsPlots +using Plots +using Plots.PlotMeasures +using Random +using JLD2 +``` + +the Cloudy modules, + +```julia +using Cloudy +using Cloudy.ParticleDistributions +using Cloudy.KernelTensors + +# Import the module that runs Cloudy +include(joinpath(@__DIR__, "DynamicalModel.jl")) +``` + +and finally the EKP packages. + +```julia +using EnsembleKalmanProcesses +using EnsembleKalmanProcesses.Observations +using EnsembleKalmanProcesses.ParameterDistributions +using EnsembleKalmanProcesses.DataContainers +``` + +The module `DynamicalModel.jl` is the forward solver; it provides a function +that runs Cloudy with a given set of parameters, + +```julia +include("DynamicalModel.jl") +``` + +#### Define the true parameters + +We define the true parameters---they are known here because this is a known +truth example. Knowing the true parameters will allow us to assess how well +Calibrate-Emulate-Sample has managed to solve the inverse problem. + +We will assume that the true particle mass distribution is a Gamma distribution, +which at time ``t = 0`` has parameters ``\phi_0 = [N_{0, 0}, k_0, \theta_0]``. We will then try to learn these parameters from observations ``y = [M_0(t_{end}), +M_1(t_{end}), M_2(t_{end})]`` of the zeroth-, first-, and second-order moments +of the distribution at time ``t_{end} > 0`` (where `t_end = 1.0` in this +example). The true parameters ``\phi_{0, \text{true}}`` are defined as follows: + +```julia +param_names = ["N0", "θ", "k"] +n_params = length(param_names) +N0_true = 300.0 # number of particles (scaling factor for Gamma distribution) +θ_true = 1.5597 # scale parameter of Gamma distribution +k_true = 0.0817 # shape parameter of Gamma distribution +ϕ_true = [N0_true, θ_true, k_true] # true parameters in constrained space +dist_true = ParticleDistributions.GammaPrimitiveParticleDistribution(ϕ_true...) +``` + +#### Define priors for the parameters + +As we are working with Bayesian methods, we treat the parameters we want to +learn as random variables whose prior distributions we specify here. The prior +distributions will behave like an "initial guess" for the likely region of +parameter space where we expect the solution to be located. +We use [`constrained_gaussian`](@ref constrained-gaussian) to add the desired scale and bounds to the prior distribution, in particular we place lower bounds to preserve positivity (and numerical stability). + +```julia +# We choose to use normal distributions to represent the prior distributions of +# the parameters in the transformed (unconstrained) space. +prior_N0 = constrained_gaussian(param_names[1], 400, 300, 0.4 * N0_true, Inf) +prior_θ = constrained_gaussian(param_names[2], 1.0, 5.0, 1e-1, Inf) +prior_k = constrained_gaussian(param_names[3], 0.2, 1.0, 1e-4, Inf) +priors = combine_distributions([prior_N0, prior_θ, prior_k]) +``` + +#### Generate (synthetic) observations +We generate synthetic observations by running Cloudy 100 times with the true +parameters (i.e., with the true initial Gamma distribution of droplet masses) and then adding noise to simulate measurement error. + +```julia +dyn_model_settings_true = DynamicalModel.ModelSettings( + kernel, dist_true, moments, tspan) + +G_t = DynamicalModel.run_dyn_model(ϕ_true, dyn_model_settings_true) +n_samples = 100 +y_t = zeros(length(G_t), n_samples) +# In a perfect model setting, the "observational noise" represents the +# internal model variability. Since Cloudy is a purely deterministic model, +# there is no straightforward way of coming up with a covariance structure +# for this internal model variability. We decide to use a diagonal +# covariance, with entries (variances) largely proportional to their +# corresponding data values, G_t +Γy = convert(Array, Diagonal([100.0, 5.0, 30.0])) +μ = zeros(length(G_t)) + +# Add noise +for i in 1:n_samples + y_t[:, i] = G_t .+ rand(MvNormal(μ, Γy)) +end + +truth = Observations.Observation(y_t, Γy, data_names) +truth_sample = truth.mean +``` + +#### Perform ensemble Kalman inversion + +We sample the initial ensemble from the prior and create the +`EnsembleKalmanProcess` object as an ensemble Kalman inversion (EKI) algorithm +using the `Inversion()` keyword. We also use the `DataMisfitController()` +learning rate scheduler. The number of ensemble members must be larger than the dimension of the parameter space to ensure a full rank ensemble covariance. + +```julia +N_ens = 50 # number of ensemble members +N_iter = 8 # number of EKI iterations +# initial parameters: n_params x N_ens +initial_params = construct_initial_ensemble(rng, priors, N_ens) +ekiobj = EnsembleKalmanProcess( + initial_params, + truth_sample, + truth.obs_noise_cov, + Inversion(), + scheduler=DataMisfitController() +) +``` + +We perform the inversion loop. Remember that within calls to `get_ϕ_final` the +EKP transformations are applied, thus the ensemble that is returned will be the +gamma distribution parameters that can be used to run the forward model, rather +than their corresponding values in the unconstrained space where the EKI takes +place. Each ensemble member is stored as a column and therefore for uses such as plotting one needs to reshape to the desired dimension. + +```julia +# Initialize a ParticleDistribution with dummy parameters. The parameters +# will then be set within `run_dyn_model` +dummy = ones(n_params) +dist_type = ParticleDistributions.GammaPrimitiveParticleDistribution(dummy...) +model_settings = DynamicalModel.ModelSettings(kernel, dist_type, moments, tspan) +# EKI iterations +for n in 1:N_iter + # Return transformed parameters in physical/constrained space + ϕ_n = get_ϕ_final(priors, ekiobj) + # Evaluate forward map + G_n = [DynamicalModel.run_dyn_model(ϕ_n[:, i], model_settings) for i in 1:N_ens] + G_ens = hcat(G_n...) # reformat + EnsembleKalmanProcesses.update_ensemble!(ekiobj, G_ens) +end +``` + + +#### Visualize and store the results of the calibration + +The optimal parameter vector determined by the ensemble Kalman inversion is the +ensemble mean of the particles after the last iteration, which is printed to +standard output. An output directory is created, where a file +`cloudy_calibrate_results.jld2` is stored, which contains all parameters and +model output from the ensemble Kalman iterations (both as +`DataContainers.DataContainer` objects), the mean and one sample of the +synthetic observations, as well as the true prameters and their priors. In +addition, an animation is produced that shows the evolution of the ensemble of +particles over subsequent iterations of the optimization, both in the +computational (unconstrained) and physical (constrained) spaces. + + +### Walkthrough of the code: `Cloudy_emulate_sample.jl` + +#### Import packages and modules + +First, we import some standard packages +```julia +using Distributions +using StatsBase +using GaussianProcesses +using LinearAlgebra +using StatsPlots +using Plots +using Plots.PlotMeasures +using Random +using JLD2 +``` + +as well as the relevant CES packages needed to construct the emulators and +perform the MCMC sampling. We also need some functionality of +`EnsembleKalmanProcesses.jl`. + +```julia +using CalibrateEmulateSample.Emulators +using CalibrateEmulateSample.MarkovChainMonteCarlo +using CalibrateEmulateSample.Utilities +using EnsembleKalmanProcesses +using EnsembleKalmanProcesses.ParameterDistributions +using EnsembleKalmanProcesses.DataContainers +``` + +#### Load the calibration results + +We will train the emulator on the input-output pairs we obtained during the +calibration. They are stored within the `EnsembleKalmanProcess` object +(`ekiobj`), which is loaded here together with the other information that was +saved in the calibration step. + +```julia +ekiobj = load(data_save_file)["eki"] +priors = load(data_save_file)["priors"] +truth_sample_mean = load(data_save_file)["truth_sample_mean"] +truth_sample = load(data_save_file)["truth_sample"] +# True parameters: +# - ϕ: in constrained space +# - θ: in unconstrained space +ϕ_true = load(data_save_file)["truth_input_constrained"] +θ_true = transform_constrained_to_unconstrained(priors, ϕ_true) +``` + +The user can choose one or both of two emulators: a Gaussian Process (GP) emulator with `GaussianProcesses.jl` interface (`gp-gpjl`) and a scalar Random Feature +(RF) interface (`rf-scalar`). See +[here](https://clima.github.io/CalibrateEmulateSample.jl/previews/PR257/examples/emulators/regression_2d_2d) +for a complete overview of the available emulators. + +```julia + cases = [ + "rf-scalar", + "gp-gpjl" # Veeeery slow predictions + ] +``` + +We first define some settings for the two emulators, e.g., the prediction type +for the GP emulator, or the number of features and hyperparameter optimizer +options for the RF emulator. The docs for GPs and RFs (TODO: add links!) explain the different options in more detail and provide some useful heuristics for how to customize the settings depending on the problem at hand. + +```julia +# These settings are the same for all Gaussian Process cases +pred_type = YType() # we want to predict data + +# These settings are the same for all Random Feature cases +n_features = 400 +nugget = 1e-8 +optimizer_options = Dict( + "verbose" => true, + "scheduler" => DataMisfitController(terminate_at = 100.0), + "cov_sample_multiplier" => 1.0, + "n_iteration" => 20, +) +``` + +We set up the learning problem specification, defining input and output dimensions, and number of data to train on, and the function g and the perturbed samples y with correlated additive noise + +Emulation is performed through the construction of an `Emulator` object from the +following components: +* a wrapper for the machine learning tool to be used as emulator +* the input-output pairs on which the emulator will be trained +* optional arguments specifying data processing and dimensionality reduction + functionality + +For `gp-gpjl`, this looks as follows: +```julia +gppackage = GPJL() +# Kernel is the sum of a squared exponential (SE), Matérn 5/2, and white noise +gp_kernel = SE(1.0, 1.0) + Mat52Ard(zeros(3), 0.0) + Noise(log(2.0)) + +# Wrapper for GP +gaussian_process = GaussianProcess( + gppackage; + kernel = gp_kernel, + prediction_type = pred_type, + noise_learn = false, +) + +# Use all input-output pairs available from the EKI iterations +input_output_pairs = get_training_points(ekiobj, + length(get_u(ekiobj))-1) + +# The data processing normalizes input data, and decorrelates output data with +# information from Γy +emulator = Emulator( + gaussian_process, + input_output_pairs, + obs_noise_cov = Γy, + normalize_inputs = true +) +``` + +And similarly for `rf-scalar`: + +```julia +kernel_structure = SeparableKernel( + LowRankFactor(n_params, nugget), + OneDimFactor() +) + +srfi = ScalarRandomFeatureInterface( + n_features, + n_params, + kernel_structure = kernel_structure, + optimizer_options = optimizer_options, +) + +retained_svd_frac = 1.0 +input_output_pairs = get_training_points(ekiobj, + length(get_u(ekiobj))-1) + +# Use the medians of the outputs as standardizing factors +norm_factors = get_standardizing_factors( + get_outputs(input_output_pairs) +) + +emulator = Emulator( + srfi, + input_output_pairs; + obs_noise_cov = Γy, + normalize_inputs = true, + standardize_outputs = true, + standardize_outputs_factors = vcat(norm_factors...), + retained_svd_frac = retained_svd_frac, + decorrelate = true # use SVD to decorrelate outputs +) +``` + +#### Train the emulator + +The emulator is trained when we combine the machine learning tool and the data +into the `Emulator` above. We must also optimize the hyperparameters: + +```julia +optimize_hyperparameters!(emulator) +``` + +To test the predictive skill of the emulator, we can e.g. compare its prediction +on the true parameters to the true data. (One could also hold out a subset of +the input-output pairs from the training and evaluate the emulator's predictions +on them). + +```julia +# Check how well the emulator predicts on the true parameters +y_mean, y_var = Emulators.predict( + emulator, + reshape(θ_true, :, 1); + transform_to_real = true +) + +println("Emulator ($(case)) prediction on true parameters: ") +println(vec(y_mean)) +println("true data: ") +println(truth_sample) # what was used as truth +``` + +The emulator predicts both a mean value and a covariance. + +### Sample the posterior distributions of the parameters + +The last step is to plug the emulator into a Markov chain Monte Carlo (MCMC) +algorithm, which is then used to produce samples from the posterior distribution +of the parameters. Essentially, the emulator acts as a stand-in for the +original forward model (which in most cases of interest is computationally +expensive to run) during the MCMC sampling process. + +We use the mean across all parameter ensembles from the EKI as the initial +parameters for the MCMC. Before running the actual MCMC chain, we determine a +good step size: +```julia +# initial values +u0 = vec(mean(get_inputs(input_output_pairs), dims = 2)) +println("initial parameters: ", u0) + +# First let's run a short chain to determine a good step size +yt_sample = truth_sample +mcmc = MCMCWrapper( + RWMHSampling(), + truth_sample, + priors, + emulator; + init_params = u0 +) + +new_step = optimize_stepsize( + mcmc; + init_stepsize = 0.1, + N = 2000, + discard_initial = 0 +) +``` + +We choose a sample size of 100'000 for the actual MCMC, discarding the first +1'000 samples as burn-in: +```julia +# Now begin the actual MCMC +println("Begin MCMC - with step size ", new_step) +chain = MarkovChainMonteCarlo.sample( + mcmc, + 100_000; + stepsize = new_step, + discard_initial = 1_000 +) +``` + +After running the MCMC, we can extract the posterior samples as follows: + +```julia +posterior = MarkovChainMonteCarlo.get_posterior(mcmc, chain) +``` + +The samples of the posterior distributions represent the ultimate output of the +CES process. By constructing histograms of these samples and comparing them with +the known true parameter values, we can evaluate the results' accuracy. Ideally, +the apex of the posterior distribution should converge near the true values, +indicating a high-quality estimation Additionally, visualizing the prior +distributions alongside the posteriors shows the distributional effected by the Bayesian learning process. + +### Results + + +### Appendix: What Does Cloudy Do? + +For the purpose of Bayesian parameter learning, the forward model can be treated +as a black box that processes input parameters to yield specific outputs. +However, for those who wish to learn more about the inner workings of Cloudy, we refer to [his paper](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022MS002994) and offer a brief outline below: + +The mathematical starting point of [Cloudy](https://github.com/CliMA/Cloudy.jl.git) is the stochastic collection equation (SCE; sometimes also called [Smoluchowski equation](https://en.wikipedia.org/wiki/Smoluchowski_coagulation_equation#:~:text=In%20statistical%20physics%2C%20the%20Smoluchowski,size%20x%20at%20time%20t.) after Marian Smoluchowski), which describes the time rate of change of ``f = f(m, t)``, the mass distribution function of liquid water droplets, due to the process of collision and coalescence. The distribution function ``f`` depends on droplet mass ``m`` and time ``t`` and is defined such that ``f(m) \text{ d}m`` denotes the number of droplets with masses in the interval $[m, m + dm]$ per unit volume. + +The stochastic collection equation is an integro-differential equation that can be written as + +```math + \frac{\partial f(m, t)}{\partial t} = \frac{1}{2} \int_{m'=0}^{\infty} f(m', t) f(m-m', t) \mathcal{C}(m', m-m')\text{d}m' - f(m, t) \int_{m'=0}^\infty f(m', t)\mathcal{C}(m, m') \text{d}m', +``` + +where ``\mathcal{C}(m', m'')`` is the collision-coalescence kernel, which encapsulates the physics of droplet-droplet interactions -- it describes the rate at which two drops of masses ``m'`` and ``m''`` come into contact and coalesce into a drop of mass ``m' + m''``. The first term on the right-hand side of the SCE describes the rate of increase of the number of drops having a mass ``m`` due to collision and coalescence of drops of masses ``m'`` and ``m-m'`` (where the factor ``\frac{1}{2} `` avoids double counting), while the second term describes the rate of reduction of drops of mass ``m`` due to collision and coalescence of drops having a mass ``m`` with other drops. + +We can rewrite the SCE in terms of the moments ``M_k`` of ``f``, which are the prognostic variables in Cloudy. They are defined by +```math + M_k = \int_0^\infty m^k f(m, t) \text{d}m +``` + +The time rate of change of the k-th moment of ``f`` is obtained by multiplying the SCE by ``m^k`` and integrating over the entire range of droplet masses (from ``m=0`` to ``\infty``), which yields +```math + \frac{\partial M_k(t)}{\partial t} = \frac{1}{2}\int_0^\infty \left((m+m')^k - m^k - {m'}^k\right) \mathcal{C}(m, m')f(m, t)f(m', t) \, \text{d}m\, \text{d}m' ~~~~~~~~ (1) +``` + +In this example, the kernel is set to be constant -- ``\mathcal{C}(m', m'') = B = \text{const}`` -- and the cloud droplet mass distribution is assumed to be a ``\text{Gamma}(k_t, \theta_t)`` distribution, scaled by a factor ``N_{0,t}`` which denotes the droplet number concentration: +```math +f(m, t) = \frac{N_{0,t}}{\Gamma(k_t)\theta_t^k} m^{k_t-1} \exp{(-m/\theta_t)} +``` +The parameter vector ``\phi_t= [N_{0,t}, k_t, \theta_t]`` changes over time (as indicated by the subscript ``t``), as the shape of the distribution evolves. In fact, there is a priori no reason to assume that the distribution would retain its Gamma shape over time, but this is a common assumption that is made in order to solve the closure problem (without this assumption, one would have to keep track of infinitely many moments of the mass distribution in order to uniquely identify the distribution ``f`` at each time step, which is obviously not practicable). + +For Gamma mass distribution functions, specifying the first three moments (``M_0``, ``M_1``, and ``M_2``) is sufficient to uniquely determine the parameter vector ``\phi_t``, hence Cloudy solves equation (1) for ``k = 0, 1, 2``. This mapping of the parameters of the initial cloud droplet mass distribution to the (zeroth-, first-, and second-order) moments of the distribution at a specified end time is done by `DynamicalModel.jl`. + + + + +### Playing Around +If you want to play around with the Cloudy examples, you can e.g. change the type or the parameters of the initial cloud droplet mass distribution (see `Cloudy.ParticleDistributions` for the available distributions), by modifying these lines: +```julia +ϕ_true = [N0_true, θ_true, k_true] +dist_true = ParticleDistributions.GammaPrimitiveParticleDistribution(ϕ_true...) +``` +(Don't forget to also change `dist_type` accordingly). + +You can also experiment with different noise covariances (`Γy`), priors, vary the number of iterations (`N_iter`) or ensemble particles (`N_ens`), etc. diff --git a/examples/deprecated/Cloudy/Cloudy_calibrate.jl b/examples/deprecated/Cloudy/Cloudy_calibrate.jl index 47d4c3a46..bff90bdff 100644 --- a/examples/deprecated/Cloudy/Cloudy_calibrate.jl +++ b/examples/deprecated/Cloudy/Cloudy_calibrate.jl @@ -1,26 +1,22 @@ # Reference the in-tree version of CalibrateEmulateSample on Julias load path include(joinpath(@__DIR__, "../..", "ci", "linkfig.jl")) -# Import the module that runs Cloudy -include(joinpath(@__DIR__, "DynamicalModel.jl")) - -# This example requires Cloudy to be installed (it's best to install the master -# branch), which can be done by: -#] add Cloudy#master -using Cloudy -using Cloudy.ParticleDistributions -using Cloudy.KernelTensors -using Cloudy -const PDistributions = Cloudy.ParticleDistributions # Import modules -using Distributions # probability distributions and associated functions +using Distributions using StatsBase using LinearAlgebra using StatsPlots using Plots -#using Plots.PlotMeasures # is this needed? +using Plots.PlotMeasures using Random -using JLD2 # is this needed? +using JLD2 + +# This example requires Cloudy to be installed. +using Cloudy +using Cloudy.ParticleDistributions +using Cloudy.KernelTensors +# Import the module that runs Cloudy +include(joinpath(@__DIR__, "DynamicalModel.jl")) # Import Ensemble Kalman Processes modules using EnsembleKalmanProcesses @@ -95,7 +91,7 @@ dist_true = ParticleDistributions.GammaPrimitiveParticleDistribution(ϕ_true...) ### # We choose to use normal distributions to represent the prior distributions of -# the parameters in the transformed (unconstrained) space. i.e log coordinates +# the parameters in the transformed (unconstrained) space. prior_N0 = constrained_gaussian(param_names[1], 400, 300, 0.4 * N0_true, Inf) prior_θ = constrained_gaussian(param_names[2], 1.0, 5.0, 1e-1, Inf) prior_k = constrained_gaussian(param_names[3], 0.2, 1.0, 1e-4, Inf) @@ -156,7 +152,7 @@ truth_sample = truth.mean # TODO: should this be yt[:, end] ### N_ens = 50 # number of ensemble members -N_iter = 8 # number of EKI iterations +N_iter = 15 # number of EKI iterations # initial parameters: n_params x N_ens initial_params = construct_initial_ensemble(rng, priors, N_ens) ekiobj = EnsembleKalmanProcess( @@ -164,6 +160,7 @@ ekiobj = EnsembleKalmanProcess( truth_sample, truth.obs_noise_cov, Inversion(), + scheduler=DataMisfitController() ) # Initialize a ParticleDistribution with dummy parameters. The parameters @@ -181,6 +178,7 @@ for n in 1:N_iter EnsembleKalmanProcesses.update_ensemble!(ekiobj, G_ens) end + # EKI results: Has the ensemble collapsed toward the truth? θ_true = transform_constrained_to_unconstrained(priors, ϕ_true) println("True parameters (unconstrained): ") @@ -218,7 +216,8 @@ u_init = get_u_prior(ekiobj) anim_eki_unconst_cloudy = @animate for i in 1:N_iter u_i = get_u(ekiobj, i) - p1 = plot(u_i[1, :], u_i[2, :], seriestype = :scatter, xlims = extrema(u_init[1, :]), ylims = extrema(u_init[2, :])) + p1 = plot(u_i[1, :], u_i[2, :], seriestype = :scatter, + xlims = extrema(u_init[1, :]), ylims = extrema(u_init[2, :])) plot!( p1, [θ_true[1]], diff --git a/examples/deprecated/Cloudy/Cloudy_emulate_sample.jl b/examples/deprecated/Cloudy/Cloudy_emulate_sample.jl index 23897e40e..d4cb64aad 100644 --- a/examples/deprecated/Cloudy/Cloudy_emulate_sample.jl +++ b/examples/deprecated/Cloudy/Cloudy_emulate_sample.jl @@ -2,24 +2,23 @@ include(joinpath(@__DIR__, "../..", "ci", "linkfig.jl")) # Import modules -using Distributions # probability distributions and associated functions +using Distributions using StatsBase using GaussianProcesses using LinearAlgebra using StatsPlots using Plots -using Plots.PlotMeasures # is this needed? +using Plots.PlotMeasures using Random -using JLD2 # is this needed? +using JLD2 # Import Calibrate-Emulate-Sample modules -#using EnsembleKalmanProcesses.DataContainers -using EnsembleKalmanProcesses -using EnsembleKalmanProcesses.ParameterDistributions -using EnsembleKalmanProcesses.DataContainers using CalibrateEmulateSample.Emulators using CalibrateEmulateSample.MarkovChainMonteCarlo using CalibrateEmulateSample.Utilities +using EnsembleKalmanProcesses +using EnsembleKalmanProcesses.ParameterDistributions +using EnsembleKalmanProcesses.DataContainers function get_standardizing_factors(data::Array{FT, 2}) where {FT} # Input: data size: N_data x N_ensembles @@ -88,29 +87,30 @@ function main() # - ϕ: in constrained space # - θ: in unconstrained space ϕ_true = load(data_save_file)["truth_input_constrained"] + θ_true = transform_constrained_to_unconstrained(priors, ϕ_true) else error("File not found: $data_save_file. Please run 'Cloudy_calibrate.jl' first.") end - θ_true = transform_constrained_to_unconstrained(priors, ϕ_true) param_names = get_name(priors) - Γy = ekiobj.obs_noise_cov n_params = length(ϕ_true) # input dimension - # Save data - #@save joinpath(output_directory, "cloudy_input_output_pairs.jld2") input_output_pairs + Γy = ekiobj.obs_noise_cov cases = [ "rf-scalar", "gp-gpjl" # Veeeery slow predictions ] + # Specify cases to run (e.g., case_mask = [2] only runs the second case) + case_mask = [1, 2] + # These settings are the same for all Gaussian Process cases - pred_type = YType() + pred_type = YType() # we want to predict data # These settings are the same for all Random Feature cases - n_features = 400 + n_features = 600 nugget = 1e-8 optimizer_options = Dict( "verbose" => true, @@ -119,12 +119,10 @@ function main() "n_iteration" => 20, ) - # Specify cases to run (e.g., case_mask = [2] only runs the second case) - case_mask = [1] - println("case mask: ") - println(case_mask) - println(cases[case_mask]) - + # We use the same input-output-pairs and normalization factors for + # Gaussian Process and Random Feature cases + input_output_pairs = get_training_points(ekiobj, + length(get_u(ekiobj))-1) norm_factors = get_standardizing_factors(get_outputs(input_output_pairs)) for case in cases[case_mask] println(" ") @@ -135,6 +133,8 @@ function main() @warn "gp-gpjl case is very slow at prediction" gppackage = GPJL() + # Kernel is the sum of a squared exponential (SE), Matérn 5/2, and + # white noise gp_kernel = SE(1.0, 1.0) + Mat52Ard(zeros(3), 0.0) + Noise(log(2.0)) gaussian_process = GaussianProcess( gppackage; @@ -143,12 +143,15 @@ function main() noise_learn = false, ) - input_output_pairs = get_training_points(ekiobj, length(get_u(ekiobj))-1) + # The data processing normalizes input data, and decorrelates + # output data with information from Γy emulator = Emulator( gaussian_process, input_output_pairs, obs_noise_cov = Γy, - normalize_inputs = true + normalize_inputs = false, + standardize_outputs = true, + standardize_outputs_factors = vcat(norm_factors...), ) elseif case == "rf-scalar" @@ -166,20 +169,6 @@ function main() ) retained_svd_frac = 1.0 - min_iter = 1 - max_iter = 5 # number of EKP iterations to use data from is at most this - @assert min_iter <= max_iter - @assert max_iter <= length(get_u(ekiobj)) - 1 - @assert min_iter >= 1 - N_iter = min(max_iter, length(get_u(ekiobj)) - 1) # number of paired iterations taken from EKP - # Get training points from the EKP iteration number in the second input term - min_iter = min(max_iter, max(1, min_iter)) - input_output_pairs = get_training_points(ekiobj, min_iter:(N_iter - 1)) - input_output_pairs_test = get_training_points( - ekiobj, N_iter:(length(get_u(ekiobj)) - 1)) # "next" iterations - norm_factors = get_standardizing_factors( - get_outputs(input_output_pairs) - ) emulator = Emulator( srfi, @@ -206,15 +195,6 @@ function main() transform_to_real = true ) - # Check how well the emulator predicts on the test input pairs (whose - # corresponding output we know, as it was calculated during EKI) - y_mean_test, y_var_test = - Emulators.predict( - emulator, - get_inputs(input_output_pairs_test), - transform_to_real = true - ) - println("Emulator ($(case)) prediction on true parameters: ") println(vec(y_mean)) println("true data: ") @@ -223,8 +203,7 @@ function main() println(sqrt.(diag(y_var[1], 0))) println("Emulator ($(case)) MSE (truth): ") println(mean((truth_sample - vec(y_mean)) .^ 2)) - #println("Emulator ($(case)) MSE (next ensemble): ") - #println(mean((get_outputs(input_output_pairs_test) - y_mean_test) .^ 2)) + ### ### Sample: Markov Chain Monte Carlo diff --git a/examples/deprecated/Cloudy/DynamicalModel.jl b/examples/deprecated/Cloudy/DynamicalModel.jl index 7967d694e..172c85a66 100644 --- a/examples/deprecated/Cloudy/DynamicalModel.jl +++ b/examples/deprecated/Cloudy/DynamicalModel.jl @@ -8,9 +8,6 @@ using Cloudy.KernelTensors using Cloudy.EquationTypes using Cloudy.Coalescence -using Sundials # CVODE_BDF() solver for ODE - - using DifferentialEquations export ModelSettings @@ -40,11 +37,12 @@ end """ run_dyn_model(ϕ::Array{FT, 1}, settings::ModelSettings{FT}) where {FT<:AbstractFloat} -Run the dynamical model (Cloudy) for the given parameter vector ϕ. +Run the dynamical model (Cloudy) for the given parameter vector ϕ=[N0,θ,k], which defines the initial distribution of droplet masses. This distribution +is assumed to be a (scaled) gamma distribution with scaling factor N0 (defining the number of particles), scale parameter θ, and shape parameter k. Return the model output, a vector of moments of the particle mass distribution at the end time of the simulation. - - `ϕ` - parameter vector of length N_parameters + - `ϕ` - parameter vector - `settings` - a ModelSettings struct """ @@ -64,25 +62,8 @@ function run_dyn_model(ϕ::Array{FT, 1}, settings::ModelSettings{FT}) where {FT moments_init = get_moments(dist_init) #dist_init = settings.dist(ϕ...) - -# ################ below is the "original" setup" -# # Numerical parameters - tol = FT(1e-7) -# -# # Set up ODE problem: dM/dt = f(M, ϕ, t) -# rhs(M, par, t) = get_int_coalescence(M, par, settings.kernel) -# ODE_par = Dict(:dist => dist_init) # ODE parameters -# prob = ODEProblem(rhs, moments_init, settings.tspan, ODE_par) -# # Solve the ODE -# sol = solve(prob, CVODE_BDF(), alg_hints = [:stiff], reltol = tol, abstol = tol) -# # -# ################ above is the "original" setup - - - ################ below is the new setup (with unreleased Cloudy code) # Set up ODE problem: dM/dt = f(M, ϕ, t) tspan = (FT(0), FT(1)) - #kernel_func = x -> 5e-3 * (x[1] + x[2]) coalescence_coeff = 1 / 3.14 / 4 / 100 kernel_func = x -> coalescence_coeff kernel = CoalescenceTensor(kernel_func, 0, FT(100)) @@ -91,13 +72,10 @@ function run_dyn_model(ϕ::Array{FT, 1}, settings::ModelSettings{FT}) where {FT :kernel => settings.kernel, :dt => FT(1) ) - #rhs = make_box_model_rhs(OneModeCoalStyle()) + rhs(m, par, t) = get_int_coalescence(OneModeCoalStyle(), m, par, par[:kernel]) prob = ODEProblem(rhs, moments_init, settings.tspan, ODE_parameters) - #sol = solve(prob, SSPRK33(), dt = ODE_parameters[:dt]) - sol = solve(prob, CVODE_BDF(), alg_hints = [:stiff], reltol = tol, abstol = tol) - # - ################ above is the new setup + sol = solve(prob, SSPRK33(), dt = ODE_parameters[:dt]) # Return moments at last time step moments_final = vcat(sol.u'...)[end, :] @@ -105,16 +83,6 @@ function run_dyn_model(ϕ::Array{FT, 1}, settings::ModelSettings{FT}) where {FT return moments_final end -""" - make_box_model_rhs(coal_type::CoalescenceStyle) - - `coal_type` type of coal source term function: OneModeCoalStyle, TwoModesCoalStyle, NumericalCoalStyle -Returns a function representing the right hand side of the ODE equation containing divergence -of coalescence source term. -""" -# TODO: update the analytical coalescence style to NOT re-allocate matrices -function make_box_model_rhs(coal_type::AnalyticalCoalStyle) - rhs(m, par, t) = get_int_coalescence(coal_type, m, par, par[:kernel]) end -end # module + From 80105e4a50de9c19b0a6b08fa384657674f74cae Mon Sep 17 00:00:00 2001 From: Melanie Date: Sun, 26 Nov 2023 19:02:09 -0500 Subject: [PATCH 05/15] Un-deprecate Cloudy example (move it one folder up; delete "deprecated" folder) --- examples/{deprecated => }/Cloudy/Cloudy_calibrate.jl | 0 examples/{deprecated => }/Cloudy/Cloudy_emulate_sample.jl | 0 examples/{deprecated => }/Cloudy/DynamicalModel.jl | 0 examples/{deprecated => }/Cloudy/Manifest.toml | 0 examples/{deprecated => }/Cloudy/Project.toml | 0 5 files changed, 0 insertions(+), 0 deletions(-) rename examples/{deprecated => }/Cloudy/Cloudy_calibrate.jl (100%) rename examples/{deprecated => }/Cloudy/Cloudy_emulate_sample.jl (100%) rename examples/{deprecated => }/Cloudy/DynamicalModel.jl (100%) rename examples/{deprecated => }/Cloudy/Manifest.toml (100%) rename examples/{deprecated => }/Cloudy/Project.toml (100%) diff --git a/examples/deprecated/Cloudy/Cloudy_calibrate.jl b/examples/Cloudy/Cloudy_calibrate.jl similarity index 100% rename from examples/deprecated/Cloudy/Cloudy_calibrate.jl rename to examples/Cloudy/Cloudy_calibrate.jl diff --git a/examples/deprecated/Cloudy/Cloudy_emulate_sample.jl b/examples/Cloudy/Cloudy_emulate_sample.jl similarity index 100% rename from examples/deprecated/Cloudy/Cloudy_emulate_sample.jl rename to examples/Cloudy/Cloudy_emulate_sample.jl diff --git a/examples/deprecated/Cloudy/DynamicalModel.jl b/examples/Cloudy/DynamicalModel.jl similarity index 100% rename from examples/deprecated/Cloudy/DynamicalModel.jl rename to examples/Cloudy/DynamicalModel.jl diff --git a/examples/deprecated/Cloudy/Manifest.toml b/examples/Cloudy/Manifest.toml similarity index 100% rename from examples/deprecated/Cloudy/Manifest.toml rename to examples/Cloudy/Manifest.toml diff --git a/examples/deprecated/Cloudy/Project.toml b/examples/Cloudy/Project.toml similarity index 100% rename from examples/deprecated/Cloudy/Project.toml rename to examples/Cloudy/Project.toml From a592f8ce04633062b5b5c783161f4712f79ccc02 Mon Sep 17 00:00:00 2001 From: Melanie Date: Tue, 28 Nov 2023 21:17:56 -0500 Subject: [PATCH 06/15] Complete docs with some pics --- docs/make.jl | 2 +- docs/src/assets/cloudy_ces_schematic.png | Bin 0 -> 154392 bytes docs/src/assets/posterior_rf-scalar_N0.png | Bin 0 -> 28757 bytes docs/src/assets/posterior_rf-scalar_k.png | Bin 0 -> 30928 bytes docs/src/assets/posterior_rf-scalar_theta.png | Bin 0 -> 29539 bytes docs/src/examples/Cloudy_example.md | 84 ++++++++++-------- 6 files changed, 47 insertions(+), 39 deletions(-) create mode 100644 docs/src/assets/cloudy_ces_schematic.png create mode 100644 docs/src/assets/posterior_rf-scalar_N0.png create mode 100644 docs/src/assets/posterior_rf-scalar_k.png create mode 100644 docs/src/assets/posterior_rf-scalar_theta.png diff --git a/docs/make.jl b/docs/make.jl index deef9fec8..bd16a2fd0 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -6,7 +6,7 @@ using Documenter #---------- -examples = ["Lorenz example" => "examples/lorenz_example.md", "Turbulence example" => "examples/edmf_example.md"] +examples = ["Lorenz example" => "examples/lorenz_example.md", "Turbulence example" => "examples/edmf_example.md", "Cloudy example" => "examples/Cloudy_example.md"] design = ["AbstractMCMC sampling API" => "API/AbstractMCMC.md"] diff --git a/docs/src/assets/cloudy_ces_schematic.png b/docs/src/assets/cloudy_ces_schematic.png new file mode 100644 index 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Lpjo7DbMb!wT@LzG literal 0 HcmV?d00001 diff --git a/docs/src/examples/Cloudy_example.md b/docs/src/examples/Cloudy_example.md index 6eea151dc..3ed475587 100755 --- a/docs/src/examples/Cloudy_example.md +++ b/docs/src/examples/Cloudy_example.md @@ -12,23 +12,34 @@ colliding and combining into bigger drops according to the droplet-droplet interactions specified by a collision-coalescence kernel. The evolution of the droplet distribution is completely determined by the shape of the initial distribution and the form of the kernel. -We will show how Calibrate-Emulate-Sample can be used to learn the parameters of -the initial cloud droplet mass distribution from observations of the moments of -that mass distribution at a later time. +We will show how Calibrate-Emulate-Sample (CES) can be used to learn the parameters of the initial cloud droplet mass distribution from observations of the moments of that mass distribution at a later time. Cloudy is used here in a "perfect model" (aka "known truth") setting, which means that the "observations" are generated by Cloudy itself, by running it with -the true parameter values---in more realistic applications, one would use actual measurements of cloud properties. +the true parameter values---in more realistic applications, one would use actual +measurements of cloud properties. + +The schematic below gives an overview of the example: The input to the CES +algorithm consists of data ``y``, the observational covariance ``Γ``, and prior +parameter distributions. The data, a vector of moments of the droplet mass +distribution, are obtained by running Cloudy with the parameters set to their +true values. The covariance is obtained from model output. The calibration stage +is performed by an ensemble Kalman inversion (EKI), in which Cloudy has to be +run once per iteration and for each ensemble member. The resulting input-output +pairs ``\{\theta_i, \mathcal{G}(\theta_i)\}_i`` are used to train an emulator +model. This emulator ``\widetilde{\mathcal{G}}(\theta)`` is cheap to evaluate; it replaces the original parameter-to-data map in the Markov chain Monte Carlo (MCMC) sampling, which produces (approximate) samples of the posterior parameter distribution. These samples are the final output of the CES algorithm. + +![Cloudy_overview](../assets/cloudy_ces_schematic.png) [This paper](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022MS002994) describes Cloudy in much more detail and shows results of experiments using -Calibrate-Emulate-Sample to learn model parameters. +CES to learn model parameters. ### Prerequisites In order to run this example, you need to install `Cloudy.jl`. The example was written using Cloudy v0.3.0, which you can install as follows: -``` +```julia pkg > add https://github.com/CliMA/Cloudy.jl.git#v0.3.0 ``` @@ -39,13 +50,13 @@ inversion; `Cloudy_emulate_sample.jl` fits an emulator and uses it to sample the posterior distributions of the parameters. Once Cloudy is installed, the example can be run from the julia REPL: ```julia -# include("Cloudy_calibrate.jl") include("Cloudy_emulate_sample.jl") ``` ### Walkthrough of the code: `Cloudy_calibrate.jl` +This file performs the calibration stage of CES. #### Import packagages and modules @@ -83,7 +94,7 @@ using EnsembleKalmanProcesses.DataContainers ``` The module `DynamicalModel.jl` is the forward solver; it provides a function -that runs Cloudy with a given set of parameters, +that runs Cloudy with a given instance of the parameter vector we want to learn. ```julia include("DynamicalModel.jl") @@ -96,8 +107,7 @@ truth example. Knowing the true parameters will allow us to assess how well Calibrate-Emulate-Sample has managed to solve the inverse problem. We will assume that the true particle mass distribution is a Gamma distribution, -which at time ``t = 0`` has parameters ``\phi_0 = [N_{0, 0}, k_0, \theta_0]``. We will then try to learn these parameters from observations ``y = [M_0(t_{end}), -M_1(t_{end}), M_2(t_{end})]`` of the zeroth-, first-, and second-order moments +which at time ``t = 0`` has parameters ``\phi_0 = [N_{0, 0}, k_0, \theta_0]``. We will then try to learn these parameters from observations ``y = [M_0(t_{end}), M_1(t_{end}), M_2(t_{end})]`` of the zeroth-, first-, and second-order moments of the distribution at time ``t_{end} > 0`` (where `t_end = 1.0` in this example). The true parameters ``\phi_{0, \text{true}}`` are defined as follows: @@ -117,7 +127,7 @@ As we are working with Bayesian methods, we treat the parameters we want to learn as random variables whose prior distributions we specify here. The prior distributions will behave like an "initial guess" for the likely region of parameter space where we expect the solution to be located. -We use [`constrained_gaussian`](@ref constrained-gaussian) to add the desired scale and bounds to the prior distribution, in particular we place lower bounds to preserve positivity (and numerical stability). +We use `constrained_gaussian` to add the desired scale and bounds to the prior distribution, in particular we place lower bounds to preserve positivity (and numerical stability). ```julia # We choose to use normal distributions to represent the prior distributions of @@ -201,7 +211,6 @@ for n in 1:N_iter end ``` - #### Visualize and store the results of the calibration The optimal parameter vector determined by the ensemble Kalman inversion is the @@ -218,6 +227,9 @@ computational (unconstrained) and physical (constrained) spaces. ### Walkthrough of the code: `Cloudy_emulate_sample.jl` +This file performs the emulation and sampling stages of the CES algorithm. + + #### Import packages and modules First, we import some standard packages @@ -234,8 +246,7 @@ using JLD2 ``` as well as the relevant CES packages needed to construct the emulators and -perform the MCMC sampling. We also need some functionality of -`EnsembleKalmanProcesses.jl`. +perform the Markov chain Monte Carlo (MCMC) sampling. We also need some functionality of `EnsembleKalmanProcesses.jl`. ```julia using CalibrateEmulateSample.Emulators @@ -271,10 +282,10 @@ The user can choose one or both of two emulators: a Gaussian Process (GP) emulat for a complete overview of the available emulators. ```julia - cases = [ - "rf-scalar", - "gp-gpjl" # Veeeery slow predictions - ] +cases = [ + "rf-scalar", + "gp-gpjl" # Veeeery slow predictions +] ``` We first define some settings for the two emulators, e.g., the prediction type @@ -296,8 +307,6 @@ optimizer_options = Dict( ) ``` -We set up the learning problem specification, defining input and output dimensions, and number of data to train on, and the function g and the perturbed samples y with correlated additive noise - Emulation is performed through the construction of an `Emulator` object from the following components: * a wrapper for the machine learning tool to be used as emulator @@ -401,15 +410,12 @@ The emulator predicts both a mean value and a covariance. ### Sample the posterior distributions of the parameters -The last step is to plug the emulator into a Markov chain Monte Carlo (MCMC) -algorithm, which is then used to produce samples from the posterior distribution -of the parameters. Essentially, the emulator acts as a stand-in for the -original forward model (which in most cases of interest is computationally -expensive to run) during the MCMC sampling process. +The last step is to plug the emulator into an MCMC algorithm, which is then used to produce samples from the posterior distribution of the parameters. Essentially, the emulator acts as a stand-in for the original forward model (which in most cases of interest is computationally expensive to run) during the MCMC sampling process. We use the mean across all parameter ensembles from the EKI as the initial parameters for the MCMC. Before running the actual MCMC chain, we determine a good step size: + ```julia # initial values u0 = vec(mean(get_inputs(input_output_pairs), dims = 2)) @@ -435,6 +441,7 @@ new_step = optimize_stepsize( We choose a sample size of 100'000 for the actual MCMC, discarding the first 1'000 samples as burn-in: + ```julia # Now begin the actual MCMC println("Begin MCMC - with step size ", new_step) @@ -455,12 +462,22 @@ posterior = MarkovChainMonteCarlo.get_posterior(mcmc, chain) The samples of the posterior distributions represent the ultimate output of the CES process. By constructing histograms of these samples and comparing them with the known true parameter values, we can evaluate the results' accuracy. Ideally, -the apex of the posterior distribution should converge near the true values, -indicating a high-quality estimation Additionally, visualizing the prior -distributions alongside the posteriors shows the distributional effected by the Bayesian learning process. +the peak of the posterior distribution should converge near the true values, +indicating a high-quality estimation. Additionally, visualizing the prior +distributions alongside the posteriors shows the distributional change effected by the Bayesian learning process. ### Results - +The following three plots show the posterior distributions obtained by the CES +algorithm, for the inverse problem of finding the parameters ``N_{0, +0}``, ``k_0``, and ``\theta_0``, which define a gamma distribution of droplet +masses in Cloudy at time ``t = 0``. The results are shown in the unbounded space +where the CES algorithm takes place. The samples posterior distributions are +shown as grey histograms, the parameters' prior distribution are shown in blue, +and the true parameter values are marked as vertical green lines. + +![posterior_N0_rf](../assets/posterior_rf-scalar_N0.png) +![posterior_theta_rf](../assets/posterior_rf-scalar_theta.png) +![posterior_k_rf](../assets/posterior_rf-scalar_k.png) ### Appendix: What Does Cloudy Do? @@ -499,12 +516,3 @@ For Gamma mass distribution functions, specifying the first three moments (``M_0 -### Playing Around -If you want to play around with the Cloudy examples, you can e.g. change the type or the parameters of the initial cloud droplet mass distribution (see `Cloudy.ParticleDistributions` for the available distributions), by modifying these lines: -```julia -ϕ_true = [N0_true, θ_true, k_true] -dist_true = ParticleDistributions.GammaPrimitiveParticleDistribution(ϕ_true...) -``` -(Don't forget to also change `dist_type` accordingly). - -You can also experiment with different noise covariances (`Γy`), priors, vary the number of iterations (`N_iter`) or ensemble particles (`N_ens`), etc. From b0c5b700b3e1a04a3eb585d5b4b357f430cb1295 Mon Sep 17 00:00:00 2001 From: Melanie Date: Sun, 3 Dec 2023 23:54:56 -0500 Subject: [PATCH 07/15] Update documentation and add plots to assets --- .../assets/cloudy_ces_schematic_resized.png | Bin 0 -> 92597 bytes docs/src/assets/eki_cloudy.gif | Bin 0 -> 186910 bytes .../assets/joint_posterior_constr_resized.png | Bin 0 -> 63228 bytes .../assets/posterior_rf-scalar_N0_resized.png | Bin 0 -> 14377 bytes .../assets/posterior_rf-scalar_k_resized.png | Bin 0 -> 19749 bytes .../posterior_rf-scalar_theta_resized.png | Bin 0 -> 12387 bytes docs/src/examples/Cloudy_example.md | 157 +- examples/Cloudy/Manifest.toml | 1560 ----------------- 8 files changed, 105 insertions(+), 1612 deletions(-) create mode 100644 docs/src/assets/cloudy_ces_schematic_resized.png create mode 100644 docs/src/assets/eki_cloudy.gif create mode 100644 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100755 --- a/docs/src/examples/Cloudy_example.md +++ b/docs/src/examples/Cloudy_example.md @@ -485,11 +485,16 @@ p_unconstr = pairplot(data_unconstr => (PairPlots.Scatter(),)) p_constr = pairplot(data_constr => (PairPlots.Scatter(),)) ``` -For the scalar RF emulator, the results (shown in the constrained/physical space) look as follows: +For the GP emulator, the results (shown in the constrained/physical space) look as follows: -![joint_posterior](../assets/joint_posterior_constr_resized.png) +![joint_posterior](../assets/joint_posterior_constr_gpjl_resized.png) -In addition, we plot the marginals of the posterior distributions: +And we can plot the same for the RF emulator: + +![joint_posterior](../assets/joint_posterior_constr_rf-scalar_resized.png) + +In addition, we plot the marginals of the posterior distributions---we are +showing them here for the GP emulator case: ```julia for idx in 1:n_params @@ -521,13 +526,15 @@ for idx in 1:n_params ax.xlabel = "Value" ax.ylabel = "Density" ``` -This is what the marginal distributions of the three parameters look like, again for the case of scalar RF and plotted in the constrained/physical space: -![posterior_N0_rf](../assets/posterior_rf-scalar_N0_resized.png) +This is what the marginal distributions of the three parameters look like, for +the case of the GP emulator, and in the constrained/physical space: + +![posterior_N0_gpjl](../assets/posterior_gp-gpjl_N0_resized.png) -![posterior_theta_rf](../assets/posterior_rf-scalar_theta_resized.png) +![posterior_theta_gpjl](../assets/posterior_gp-gpjl_theta_resized.png) -![posterior_k_rf](../assets/posterior_rf-scalar_k_resized.png) +![posterior_k_gpjl](../assets/posterior_gp-gpjl_k_resized.png) Here, the posterior distributions are shown as orange histograms, the prior distribution are shown as grey histograms (though with the exception of the parmaeter `k`, they are barely visible), and the true parameter values are marked as vertical purple lines. diff --git a/examples/Cloudy/Cloudy_emulate_sample.jl b/examples/Cloudy/Cloudy_emulate_sample.jl index d49715b90..0683e33ed 100644 --- a/examples/Cloudy/Cloudy_emulate_sample.jl +++ b/examples/Cloudy/Cloudy_emulate_sample.jl @@ -104,7 +104,7 @@ function main() ] # Specify cases to run (e.g., case_mask = [2] only runs the second case) - case_mask = [2] + case_mask = [1, 2] # These settings are the same for all Gaussian Process cases pred_type = YType() # we want to predict data @@ -172,7 +172,6 @@ function main() mlt, input_output_pairs, obs_noise_cov = Γy, - #normalize_inputs = false, standardize_outputs = true, standardize_outputs_factors = vcat(norm_factors...), ) From fef35d9b3e7d6f3a95de9d017885c086abb6ab2f Mon Sep 17 00:00:00 2001 From: Melanie Date: Thu, 7 Dec 2023 10:51:38 -0500 Subject: [PATCH 11/15] Finalize PR#253 (vector RF case to be done in separate PR) --- .dev/Manifest.toml | 216 ++++++++++++++++++ docs/make.jl | 6 +- ...c_resized.png => cloudy_ces_schematic.png} | Bin .../assets/{eki_cloudy.gif => cloudy_eki.gif} | Bin ..._marginal_posterior_constr_gp-gpjl_N0.png} | Bin ...y_marginal_posterior_constr_gp-gpjl_k.png} | Bin ...rginal_posterior_constr_gp-gpjl_theta.png} | Bin ...udy_pairplot_posterior_constr_gp-gpjl.png} | Bin ...y_pairplot_posterior_constr_rf-scalar.png} | Bin docs/src/examples/Cloudy_example.md | 23 +- examples/Cloudy/Cloudy_calibrate.jl | 55 ++--- examples/Cloudy/Cloudy_emulate_sample.jl | 86 ++----- examples/Cloudy/DynamicalModel.jl | 8 +- examples/Cloudy/Project.toml | 12 +- 14 files changed, 280 insertions(+), 126 deletions(-) create mode 100644 .dev/Manifest.toml rename docs/src/assets/{cloudy_ces_schematic_resized.png => cloudy_ces_schematic.png} (100%) rename docs/src/assets/{eki_cloudy.gif => cloudy_eki.gif} (100%) rename docs/src/assets/{posterior_gp-gpjl_N0_resized.png => cloudy_marginal_posterior_constr_gp-gpjl_N0.png} (100%) rename docs/src/assets/{posterior_gp-gpjl_k_resized.png => cloudy_marginal_posterior_constr_gp-gpjl_k.png} (100%) rename docs/src/assets/{posterior_gp-gpjl_theta_resized.png => cloudy_marginal_posterior_constr_gp-gpjl_theta.png} (100%) rename docs/src/assets/{joint_posterior_constr_gpjl_resized.png => cloudy_pairplot_posterior_constr_gp-gpjl.png} (100%) rename docs/src/assets/{joint_posterior_constr_rf-scalar_resized.png => cloudy_pairplot_posterior_constr_rf-scalar.png} (100%) diff --git a/.dev/Manifest.toml b/.dev/Manifest.toml new file mode 100644 index 000000000..3fe61baab --- /dev/null +++ b/.dev/Manifest.toml @@ -0,0 +1,216 @@ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.9.3" +manifest_format = "2.0" +project_hash = "48ccf565f8f6fe0b682f40b453b39e32c209f422" + +[[deps.ArgTools]] +uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" +version = "1.1.1" + +[[deps.Artifacts]] +uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" + +[[deps.Base64]] +uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f" + 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+version = "0.5.26" + +[[deps.URIs]] +git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b" +uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4" +version = "1.5.1" + +[[deps.UUIDs]] +deps = ["Random", "SHA"] +uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4" + +[[deps.Unicode]] +uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" + +[[deps.Zlib_jll]] +deps = ["Libdl"] +uuid = "83775a58-1f1d-513f-b197-d71354ab007a" +version = "1.2.13+0" + +[[deps.nghttp2_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" +version = "1.48.0+0" + +[[deps.p7zip_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" +version = "17.4.0+0" diff --git a/docs/make.jl b/docs/make.jl index bd16a2fd0..678c92253 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -6,7 +6,11 @@ using Documenter #---------- -examples = ["Lorenz example" => "examples/lorenz_example.md", "Turbulence example" => "examples/edmf_example.md", "Cloudy example" => "examples/Cloudy_example.md"] +examples = [ + "Lorenz example" => "examples/lorenz_example.md", + "Turbulence example" => "examples/edmf_example.md", + "Cloudy example" => "examples/Cloudy_example.md", +] design = ["AbstractMCMC sampling API" => "API/AbstractMCMC.md"] diff --git a/docs/src/assets/cloudy_ces_schematic_resized.png b/docs/src/assets/cloudy_ces_schematic.png similarity index 100% rename from docs/src/assets/cloudy_ces_schematic_resized.png rename to docs/src/assets/cloudy_ces_schematic.png diff --git a/docs/src/assets/eki_cloudy.gif b/docs/src/assets/cloudy_eki.gif similarity index 100% rename from docs/src/assets/eki_cloudy.gif rename to docs/src/assets/cloudy_eki.gif diff --git a/docs/src/assets/posterior_gp-gpjl_N0_resized.png b/docs/src/assets/cloudy_marginal_posterior_constr_gp-gpjl_N0.png similarity index 100% rename from docs/src/assets/posterior_gp-gpjl_N0_resized.png rename to docs/src/assets/cloudy_marginal_posterior_constr_gp-gpjl_N0.png diff --git a/docs/src/assets/posterior_gp-gpjl_k_resized.png b/docs/src/assets/cloudy_marginal_posterior_constr_gp-gpjl_k.png similarity index 100% rename from docs/src/assets/posterior_gp-gpjl_k_resized.png rename to docs/src/assets/cloudy_marginal_posterior_constr_gp-gpjl_k.png diff --git a/docs/src/assets/posterior_gp-gpjl_theta_resized.png b/docs/src/assets/cloudy_marginal_posterior_constr_gp-gpjl_theta.png similarity index 100% rename from docs/src/assets/posterior_gp-gpjl_theta_resized.png rename to docs/src/assets/cloudy_marginal_posterior_constr_gp-gpjl_theta.png diff --git a/docs/src/assets/joint_posterior_constr_gpjl_resized.png b/docs/src/assets/cloudy_pairplot_posterior_constr_gp-gpjl.png similarity index 100% rename from docs/src/assets/joint_posterior_constr_gpjl_resized.png rename to docs/src/assets/cloudy_pairplot_posterior_constr_gp-gpjl.png diff --git a/docs/src/assets/joint_posterior_constr_rf-scalar_resized.png b/docs/src/assets/cloudy_pairplot_posterior_constr_rf-scalar.png similarity index 100% rename from docs/src/assets/joint_posterior_constr_rf-scalar_resized.png rename to docs/src/assets/cloudy_pairplot_posterior_constr_rf-scalar.png diff --git a/docs/src/examples/Cloudy_example.md b/docs/src/examples/Cloudy_example.md index 50f42e729..3ae0e50a2 100755 --- a/docs/src/examples/Cloudy_example.md +++ b/docs/src/examples/Cloudy_example.md @@ -21,7 +21,7 @@ measurements of cloud properties. The following schematic gives an overview of the example: -![cloudy_schematic](../assets/cloudy_ces_schematic_resized.png) +![cloudy_schematic](../assets/cloudy_ces_schematic.png) The input to the CES algorithm consists of data ``y``, the observational covariance ``Γ``, and prior parameter distributions. The data, a vector of moments of the droplet mass distribution, are obtained by running Cloudy with the parameters set to their true values. The covariance is obtained from model output. The calibration stage is performed by an ensemble Kalman inversion (EKI), in which Cloudy has to be run once per iteration and for each ensemble member. The resulting input-output pairs ``\{\theta_i, \mathcal{G}(\theta_i)\}_i`` are used to train an emulator model. This emulator ``\widetilde{\mathcal{G}}(\theta)`` is cheap to evaluate; it replaces the original parameter-to-data map in the Markov chain Monte Carlo (MCMC) sampling, which produces (approximate) samples of the posterior parameter distribution. These samples are the final output of the CES algorithm. @@ -29,14 +29,6 @@ The input to the CES algorithm consists of data ``y``, the observational covaria CES to learn model parameters. -### Prerequisites - -In order to run this example, you need to install `Cloudy.jl`. The example was -written using Cloudy v0.3.0, which you can install as follows: -```julia -pkg > add https://github.com/CliMA/Cloudy.jl.git#v0.3.0 -``` - ### Running the example `Cloudy_calibrate.jl` performs the calibration using ensemble Kalman @@ -140,7 +132,6 @@ The plot recipe for `ParameterDistribution` types allows for quick visualization ```julia # Plot the priors p = plot(priors, constrained=false) -savefig(p, output_directory * "cloudy_priors.png") ``` ![priors](../assets/cloudy_priors.png) @@ -232,7 +223,7 @@ particles over subsequent iterations of the optimization, both in the computational (unconstrained) and physical (constrained) spaces. -![eki_iterations_animation](../assets/eki_cloudy.gif) +![eki_iterations_animation](../assets/cloudy_eki.gif) ### Walkthrough of the code: `Cloudy_emulate_sample.jl` @@ -487,11 +478,11 @@ p_constr = pairplot(data_constr => (PairPlots.Scatter(),)) For the GP emulator, the results (shown in the constrained/physical space) look as follows: -![joint_posterior](../assets/joint_posterior_constr_gpjl_resized.png) +![pairplot_posterior_gpjl](../assets/cloudy_pairplot_posterior_constr_gp-gpjl.png) And we can plot the same for the RF emulator: -![joint_posterior](../assets/joint_posterior_constr_rf-scalar_resized.png) +![pairplot_posterior_rf-scalar](../assets/cloudy_pairplot_posterior_constr_rf-scalar.png) In addition, we plot the marginals of the posterior distributions---we are showing them here for the GP emulator case: @@ -530,11 +521,11 @@ for idx in 1:n_params This is what the marginal distributions of the three parameters look like, for the case of the GP emulator, and in the constrained/physical space: -![posterior_N0_gpjl](../assets/posterior_gp-gpjl_N0_resized.png) +![posterior_N0_gpjl](../assets/cloudy_marginal_posterior_constr_gp-gpjl_N0.png) -![posterior_theta_gpjl](../assets/posterior_gp-gpjl_theta_resized.png) +![posterior_theta_gpjl](../assets/cloudy_marginal_posterior_constr_gp-gpjl_theta.png) -![posterior_k_gpjl](../assets/posterior_gp-gpjl_k_resized.png) +![posterior_k_gpjl](../assets/cloudy_marginal_posterior_constr_gp-gpjl_k.png) Here, the posterior distributions are shown as orange histograms, the prior distribution are shown as grey histograms (though with the exception of the parmaeter `k`, they are barely visible), and the true parameter values are marked as vertical purple lines. diff --git a/examples/Cloudy/Cloudy_calibrate.jl b/examples/Cloudy/Cloudy_calibrate.jl index 8171b0b51..03f30577e 100644 --- a/examples/Cloudy/Cloudy_calibrate.jl +++ b/examples/Cloudy/Cloudy_calibrate.jl @@ -93,7 +93,7 @@ prior_θ = constrained_gaussian(param_names[2], 1.0, 5.0, 1e-1, Inf) prior_k = constrained_gaussian(param_names[3], 0.2, 1.0, 1e-4, Inf) priors = combine_distributions([prior_N0, prior_θ, prior_k]) # Plot the priors -p = plot(priors, constrained=false) +p = plot(priors, constrained = false) savefig(p, output_directory * "cloudy_priors.png") ### @@ -120,8 +120,7 @@ kernel = Cloudy.KernelTensors.CoalescenceTensor(kernel_func, 0, 300.0) ### Generate (artificial) truth samples ### -dyn_model_settings_true = DynamicalModel.ModelSettings( - kernel, dist_true, moments, tspan) +dyn_model_settings_true = DynamicalModel.ModelSettings(kernel, dist_true, moments, tspan) G_t = DynamicalModel.run_dyn_model(ϕ_true, dyn_model_settings_true) n_samples = 100 @@ -141,7 +140,7 @@ for i in 1:n_samples end truth = Observations.Observation(y_t, Γy, data_names) -truth_sample = truth.mean # TODO: should this be yt[:, end] +truth_sample = truth.mean ### @@ -157,7 +156,7 @@ ekiobj = EnsembleKalmanProcess( truth_sample, truth.obs_noise_cov, Inversion(), - scheduler=DataMisfitController() + scheduler = DataMisfitController(), ) # Initialize a ParticleDistribution with dummy parameters. The parameters @@ -208,11 +207,10 @@ save( gr(size = (1200, 400)) u_init = get_u_prior(ekiobj) -anim_eki_unconst_cloudy = @animate for i in 1:(N_iter-1) +anim_eki_unconst_cloudy = @animate for i in 1:(N_iter - 1) u_i = get_u(ekiobj, i) - p1 = plot(u_i[1, :], u_i[2, :], seriestype = :scatter, - xlims = extrema(u_init[1, :]), ylims = extrema(u_init[2, :])) + p1 = plot(u_i[1, :], u_i[2, :], seriestype = :scatter, xlims = extrema(u_init[1, :]), ylims = extrema(u_init[2, :])) plot!( p1, [θ_true[1]], @@ -225,11 +223,9 @@ anim_eki_unconst_cloudy = @animate for i in 1:(N_iter-1) margin = 5mm, title = "EKI iteration = " * string(i), ) - plot!(p1, [θ_true[2]], seriestype = "hline", linestyle = :dash, - linecolor = :red, label = "optimum") + plot!(p1, [θ_true[2]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") - p2 = plot(u_i[2, :], u_i[3, :], seriestype = :scatter, - xlims = extrema(u_init[2, :]), ylims = extrema(u_init[3, :])) + p2 = plot(u_i[2, :], u_i[3, :], seriestype = :scatter, xlims = extrema(u_init[2, :]), ylims = extrema(u_init[3, :])) plot!( p2, [θ_true[2]], @@ -243,11 +239,9 @@ anim_eki_unconst_cloudy = @animate for i in 1:(N_iter-1) title = "EKI iteration = " * string(i), ) - plot!(p2, [θ_true[3]], seriestype = "hline", linestyle = :dash, - linecolor = :red, label = "optimum") + plot!(p2, [θ_true[3]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") - p3 = plot(u_i[3, :], u_i[1, :], seriestype = :scatter, - xlims = extrema(u_init[3, :]), ylims = extrema(u_init[1, :])) + p3 = plot(u_i[3, :], u_i[1, :], seriestype = :scatter, xlims = extrema(u_init[3, :]), ylims = extrema(u_init[1, :])) plot!( p3, [θ_true[3]], @@ -261,22 +255,19 @@ anim_eki_unconst_cloudy = @animate for i in 1:(N_iter-1) title = "EKI iteration = " * string(i), ) - plot!(p3, [θ_true[1]], seriestype = "hline", linestyle = :dash, - linecolor = :red, label = "optimum") + plot!(p3, [θ_true[1]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") p = plot(p1, p2, p3, layout = (1, 3)) end -gif(anim_eki_unconst_cloudy, - joinpath(output_directory, "eki_unconst_cloudy.gif"), fps = 1) # hide +gif(anim_eki_unconst_cloudy, joinpath(output_directory, "cloudy_eki_unconstr.gif"), fps = 1) # hide # Plots in the constrained space ϕ_init = transform_unconstrained_to_constrained(priors, u_init) -anim_eki_cloudy = @animate for i in 1:(N_iter-1) +anim_eki_cloudy = @animate for i in 1:(N_iter - 1) ϕ_i = get_ϕ(priors, ekiobj, i) - p1 = plot(ϕ_i[1, :], ϕ_i[2, :], seriestype = :scatter, - xlims = extrema(ϕ_init[1, :]), ylims = extrema(ϕ_init[2, :])) + p1 = plot(ϕ_i[1, :], ϕ_i[2, :], seriestype = :scatter, xlims = extrema(ϕ_init[1, :]), ylims = extrema(ϕ_init[2, :])) plot!( p1, [ϕ_true[1]], @@ -290,11 +281,9 @@ anim_eki_cloudy = @animate for i in 1:(N_iter-1) title = "EKI iteration = " * string(i), ) - plot!(p1, [ϕ_true[2]], seriestype = "hline", linestyle = :dash, - linecolor = :red, label = "optimum") + plot!(p1, [ϕ_true[2]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") - p2 = plot(ϕ_i[2, :], ϕ_i[3, :], seriestype = :scatter, - xlims = extrema(ϕ_init[2, :]), ylims = extrema(ϕ_init[3, :])) + p2 = plot(ϕ_i[2, :], ϕ_i[3, :], seriestype = :scatter, xlims = extrema(ϕ_init[2, :]), ylims = extrema(ϕ_init[3, :])) plot!( p2, @@ -309,11 +298,9 @@ anim_eki_cloudy = @animate for i in 1:(N_iter-1) title = "EKI iteration = " * string(i), ) - plot!(p2, [ϕ_true[3]], seriestype = "hline", linestyle = :dash, - linecolor = :red, label = "optimum") + plot!(p2, [ϕ_true[3]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") - p3 = plot(ϕ_i[3, :], ϕ_i[1, :], seriestype = :scatter, - xlims = extrema(ϕ_init[3, :]), ylims = extrema(ϕ_init[1, :])) + p3 = plot(ϕ_i[3, :], ϕ_i[1, :], seriestype = :scatter, xlims = extrema(ϕ_init[3, :]), ylims = extrema(ϕ_init[1, :])) plot!( p3, [ϕ_true[3]], @@ -326,12 +313,10 @@ anim_eki_cloudy = @animate for i in 1:(N_iter-1) label = false, title = "EKI iteration = " * string(i), ) - plot!(p3, [ϕ_true[1]], seriestype = "hline", linestyle = :dash, - linecolor = :red, label = "optimum") + plot!(p3, [ϕ_true[1]], seriestype = "hline", linestyle = :dash, linecolor = :red, label = "optimum") p = plot(p1, p2, p3, layout = (1, 3)) end -gif(anim_eki_cloudy, - joinpath(output_directory, "eki_cloudy.gif"), fps = 1) # hide +gif(anim_eki_cloudy, joinpath(output_directory, "cloudy_eki_constr.gif"), fps = 1) # hide diff --git a/examples/Cloudy/Cloudy_emulate_sample.jl b/examples/Cloudy/Cloudy_emulate_sample.jl index 0683e33ed..188ebc825 100644 --- a/examples/Cloudy/Cloudy_emulate_sample.jl +++ b/examples/Cloudy/Cloudy_emulate_sample.jl @@ -71,10 +71,7 @@ function main() # The calibration results must be produced by running Cloudy_calibrate.jl # before running Cloudy_emulate_sample.jl - data_save_file = joinpath( - output_directory, - "cloudy_calibrate_results.jld2" - ) + data_save_file = joinpath(output_directory, "cloudy_calibrate_results.jld2") # Check if the file exists before loading if isfile(data_save_file) @@ -100,7 +97,7 @@ function main() cases = [ "rf-scalar", - "gp-gpjl" # Veeeery slow predictions + "gp-gpjl", # Veeeery slow predictions ] # Specify cases to run (e.g., case_mask = [2] only runs the second case) @@ -121,8 +118,7 @@ function main() # We use the same input-output-pairs and normalization factors for # Gaussian Process and Random Feature cases - input_output_pairs = get_training_points(ekiobj, - length(get_u(ekiobj))-1) + input_output_pairs = get_training_points(ekiobj, length(get_u(ekiobj)) - 1) norm_factors = get_standardizing_factors(get_outputs(input_output_pairs)) for case in cases[case_mask] @@ -139,19 +135,11 @@ function main() gp_kernel = SE(1.0, 1.0) + Mat52Ard(zeros(3), 0.0) + Noise(log(2.0)) # Define machine learning tool - mlt = GaussianProcess( - gppackage; - kernel = gp_kernel, - prediction_type = pred_type, - noise_learn = false, - ) + mlt = GaussianProcess(gppackage; kernel = gp_kernel, prediction_type = pred_type, noise_learn = false) elseif case == "rf-scalar" - kernel_structure = SeparableKernel( - LowRankFactor(n_params, nugget), - OneDimFactor() - ) + kernel_structure = SeparableKernel(LowRankFactor(n_params, nugget), OneDimFactor()) # Define machine learning tool mlt = ScalarRandomFeatureInterface( @@ -179,11 +167,7 @@ function main() optimize_hyperparameters!(emulator) # Check how well the emulator predicts on the true parameters - y_mean, y_var = Emulators.predict( - emulator, - reshape(θ_true, :, 1); - transform_to_real = true - ) + y_mean, y_var = Emulators.predict(emulator, reshape(θ_true, :, 1); transform_to_real = true) println("Emulator ($(case)) prediction on true parameters: ") println(vec(y_mean)) @@ -205,29 +189,13 @@ function main() # First let's run a short chain to determine a good step size yt_sample = truth_sample - mcmc = MCMCWrapper( - RWMHSampling(), - yt_sample, - priors, - emulator; - init_params = u0 - ) + mcmc = MCMCWrapper(RWMHSampling(), yt_sample, priors, emulator; init_params = u0) - new_step = optimize_stepsize( - mcmc; - init_stepsize = 0.1, - N = 2000, - discard_initial = 0 - ) + new_step = optimize_stepsize(mcmc; init_stepsize = 0.1, N = 2000, discard_initial = 0) # Now begin the actual MCMC println("Begin MCMC - with step size ", new_step) - chain = MarkovChainMonteCarlo.sample( - mcmc, - 100_000; - stepsize = new_step, - discard_initial = 1_000 - ) + chain = MarkovChainMonteCarlo.sample(mcmc, 100_000; stepsize = new_step, discard_initial = 1_000) posterior = MarkovChainMonteCarlo.get_posterior(mcmc, chain) @@ -240,29 +208,22 @@ function main() # Prior samples prior_samples_unconstr = sample(rng, priors, Int(1e4)) - prior_samples_constr = transform_unconstrained_to_constrained( - priors, prior_samples_unconstr) + prior_samples_constr = transform_unconstrained_to_constrained(priors, prior_samples_unconstr) # Posterior samples - posterior_samples_unconstr = - vcat([get_distribution(posterior)[name] - for name in get_name(posterior)]...) # samples are columns + posterior_samples_unconstr = vcat([get_distribution(posterior)[name] for name in get_name(posterior)]...) # samples are columns posterior_samples_constr = - mapslices(x -> transform_unconstrained_to_constrained(posterior, x), - posterior_samples_unconstr, dims = 1) + mapslices(x -> transform_unconstrained_to_constrained(posterior, x), posterior_samples_unconstr, dims = 1) # Make pair plots of the posterior distributions in the unconstrained # and in the constrained space (this uses `PairPlots.jl`) - figpath_unconstr = joinpath(output_directory, - "joint_posterior_unconstr_" * case * ".png") - figpath_constr = joinpath(output_directory, - "joint_posterior_constr.png_" * case * ".png") + figpath_unconstr = joinpath(output_directory, "joint_posterior_unconstr_" * case * ".png") + figpath_constr = joinpath(output_directory, "joint_posterior_constr.png_" * case * ".png") labels = get_name(posterior) - data_unconstr = (; [(Symbol(labels[i]), - posterior_samples_unconstr[i, :]) for i in 1:length(labels)]...) - data_constr = (; [(Symbol(labels[i]), - posterior_samples_constr[i, :]) for i in 1:length(labels)]...) + data_unconstr = + (; [(Symbol(labels[i]), pairplot_posterior_samples_unconstr[i, :]) for i in 1:length(labels)]...) + data_constr = (; [(Symbol(labels[i]), pairplot_posterior_samples_constr[i, :]) for i in 1:length(labels)]...) p_unconstr = pairplot(data_unconstr => (PairPlots.Scatter(),)) p_constr = pairplot(data_constr => (PairPlots.Scatter(),)) @@ -270,7 +231,7 @@ function main() save(figpath_constr, p_constr) # Plot the marginal posterior distributions together with the priors - # and the true parameter values (in the constrained space) + # and the true parameter values (we'll do that in the constrained space) n_params = length(get_name(posterior)) for idx in 1:n_params @@ -284,16 +245,13 @@ function main() ax = Axis(fig[1, 1]) # Histogram for posterior samples - hist!(ax, posterior_samples_constr[idx, :], bins = 100, - color = :darkorange, label = "posterior") + hist!(ax, posterior_samples_constr[idx, :], bins = 100, color = :darkorange, label = "posterior") # Plotting the prior distribution - hist!(ax, prior_samples_constr[idx, :], bins = 10000, - color = :slategray) + hist!(ax, prior_samples_constr[idx, :], bins = 10000, color = :slategray) # Adding a vertical line for the true value - vlines!(ax, [ϕ_true[idx]], color = :indigo, linewidth = 2.6, - label = "true " * param_names[idx]) + vlines!(ax, [ϕ_true[idx]], color = :indigo, linewidth = 2.6, label = "true " * param_names[idx]) xlims!(ax, xmin, xmax) ylims!(ax, 0, nothing) @@ -306,7 +264,7 @@ function main() # Save the figure (marginal posterior distribution in constrained # space) - figname = "posterior_" * case * "_" * param_names[idx] * ".png" + figname = "marginal_posterior_constr_" * case * "_" * param_names[idx] * ".png" figpath_marg_constr = joinpath(output_directory, figname) save(figpath_marg_constr, fig) diff --git a/examples/Cloudy/DynamicalModel.jl b/examples/Cloudy/DynamicalModel.jl index 099d47d29..f8b4d807e 100644 --- a/examples/Cloudy/DynamicalModel.jl +++ b/examples/Cloudy/DynamicalModel.jl @@ -57,11 +57,7 @@ function run_dyn_model(ϕ::Array{FT, 1}, settings::ModelSettings{FT}) where {FT coalescence_coeff = 1 / 3.14 / 4 / 100 kernel_func = x -> coalescence_coeff kernel = CoalescenceTensor(kernel_func, 0, FT(100)) - ODE_parameters = Dict( - :dist => [dist_init], - :kernel => settings.kernel, - :dt => FT(1) - ) + ODE_parameters = Dict(:dist => [dist_init], :kernel => settings.kernel, :dt => FT(1)) rhs(m, par, t) = get_int_coalescence(OneModeCoalStyle(), m, par, par[:kernel]) prob = ODEProblem(rhs, moments_init, settings.tspan, ODE_parameters) @@ -74,5 +70,3 @@ function run_dyn_model(ϕ::Array{FT, 1}, settings::ModelSettings{FT}) where {FT end end - - diff --git a/examples/Cloudy/Project.toml b/examples/Cloudy/Project.toml index f48810fef..bbfb0b9b9 100644 --- a/examples/Cloudy/Project.toml +++ b/examples/Cloudy/Project.toml @@ -1,18 +1,24 @@ [deps] +CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" Cloudy = "9e3b23bb-e7cc-4b94-886c-65de2234ba87" -Conda = "8f4d0f93-b110-5947-807f-2305c1781a2d" DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa" Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae" -FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341" GaussianProcesses = "891a1506-143c-57d2-908e-e1f8e92e6de9" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +PairPlots = "43a3c2be-4208-490b-832a-a21dcd55d7da" Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91" StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd" +CalibrateEmulateSample = "95e48a1f-0bec-4818-9538-3db4340308e3" +EnsembleKalmanProcesses = "aa8a2aa5-91d8-4396-bcef-d4f2ec43552d" +JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819" +Cloudy = "9e3b23bb-e7cc-4b94-886c-65de2234ba87" + [compat] -julia = "~1.6" FFTW = "= 1.3.0" +julia = "~1.6" +Cloudy = "0.3" From 35fa12a2cd67c4f17d9deaa0119efed8d3e5fe7e Mon Sep 17 00:00:00 2001 From: Melanie Date: Thu, 7 Dec 2023 16:25:16 -0500 Subject: [PATCH 12/15] Fix typos --- examples/Cloudy/Cloudy_emulate_sample.jl | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/examples/Cloudy/Cloudy_emulate_sample.jl b/examples/Cloudy/Cloudy_emulate_sample.jl index 188ebc825..0b88b6714 100644 --- a/examples/Cloudy/Cloudy_emulate_sample.jl +++ b/examples/Cloudy/Cloudy_emulate_sample.jl @@ -93,6 +93,7 @@ function main() param_names = get_name(priors) n_params = length(ϕ_true) # input dimension + Γy = ekiobj.obs_noise_cov cases = [ @@ -217,13 +218,13 @@ function main() # Make pair plots of the posterior distributions in the unconstrained # and in the constrained space (this uses `PairPlots.jl`) - figpath_unconstr = joinpath(output_directory, "joint_posterior_unconstr_" * case * ".png") - figpath_constr = joinpath(output_directory, "joint_posterior_constr.png_" * case * ".png") + figpath_unconstr = joinpath(output_directory, "pairplot_posterior_unconstr_" * case * ".png") + figpath_constr = joinpath(output_directory, "pairplot_posterior_constr.png_" * case * ".png") labels = get_name(posterior) data_unconstr = - (; [(Symbol(labels[i]), pairplot_posterior_samples_unconstr[i, :]) for i in 1:length(labels)]...) - data_constr = (; [(Symbol(labels[i]), pairplot_posterior_samples_constr[i, :]) for i in 1:length(labels)]...) + (; [(Symbol(labels[i]), posterior_samples_unconstr[i, :]) for i in 1:length(labels)]...) + data_constr = (; [(Symbol(labels[i]), posterior_samples_constr[i, :]) for i in 1:length(labels)]...) p_unconstr = pairplot(data_unconstr => (PairPlots.Scatter(),)) p_constr = pairplot(data_constr => (PairPlots.Scatter(),)) @@ -232,7 +233,6 @@ function main() # Plot the marginal posterior distributions together with the priors # and the true parameter values (we'll do that in the constrained space) - n_params = length(get_name(posterior)) for idx in 1:n_params From 892d381765939ac3172ab167f3c5ab4be2ca20d6 Mon Sep 17 00:00:00 2001 From: odunbar Date: Fri, 8 Dec 2023 14:22:50 -0800 Subject: [PATCH 13/15] rm formatter Manifest. 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data_unconstr = - (; [(Symbol(labels[i]), posterior_samples_unconstr[i, :]) for i in 1:length(labels)]...) + data_unconstr = (; [(Symbol(labels[i]), posterior_samples_unconstr[i, :]) for i in 1:length(labels)]...) data_constr = (; [(Symbol(labels[i]), posterior_samples_constr[i, :]) for i in 1:length(labels)]...) p_unconstr = pairplot(data_unconstr => (PairPlots.Scatter(),)) From 9e99992f05d1a64b4ea8bcc0efc1060de169027f Mon Sep 17 00:00:00 2001 From: odunbar Date: Mon, 11 Dec 2023 11:44:20 -0800 Subject: [PATCH 14/15] try with gpjl -> skljl --- test/Emulator/runtests.jl | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/test/Emulator/runtests.jl b/test/Emulator/runtests.jl index b062a822d..3f5e3b640 100644 --- a/test/Emulator/runtests.jl +++ b/test/Emulator/runtests.jl @@ -34,7 +34,7 @@ function constructor_tests( ) #build a known type, with defaults - gp = GaussianProcess(GPJL()) + gp = GaussianProcess(SKLJL()) emulator = Emulator( gp, iopairs, @@ -50,7 +50,7 @@ function constructor_tests( @test test_decomp.Vt == decomposition.Vt @test test_decomp.S == decomposition.S - gp = GaussianProcess(GPJL()) + gp = GaussianProcess(SKLJL()) emulator2 = Emulator( gp, iopairs, @@ -65,7 +65,7 @@ function constructor_tests( @test train_inputs2 == norm_inputs # reverse standardise - gp = GaussianProcess(GPJL()) + gp = GaussianProcess(SKLJL()) emulator3 = Emulator( gp, iopairs, @@ -174,7 +174,7 @@ end constructor_tests(iopairs, Σ, norm_factors, decomposition) # truncation - only test here, where singular value of Σ differ - gp = GaussianProcess(GPJL()) + gp = GaussianProcess(SKLJL()) emulator4 = Emulator( gp, iopairs, From e34b5f065433df4e633674b52bec0788c04febdb Mon Sep 17 00:00:00 2001 From: odunbar Date: Mon, 11 Dec 2023 11:54:40 -0800 Subject: [PATCH 15/15] did not work, reverting and opening new PR for fix --- test/Emulator/runtests.jl | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/test/Emulator/runtests.jl b/test/Emulator/runtests.jl index 3f5e3b640..b062a822d 100644 --- a/test/Emulator/runtests.jl +++ b/test/Emulator/runtests.jl @@ -34,7 +34,7 @@ function constructor_tests( ) #build a known type, with defaults - gp = GaussianProcess(SKLJL()) + gp = GaussianProcess(GPJL()) emulator = Emulator( gp, iopairs, @@ -50,7 +50,7 @@ function constructor_tests( @test test_decomp.Vt == decomposition.Vt @test test_decomp.S == decomposition.S - gp = GaussianProcess(SKLJL()) + gp = GaussianProcess(GPJL()) emulator2 = Emulator( gp, iopairs, @@ -65,7 +65,7 @@ function constructor_tests( @test train_inputs2 == norm_inputs # reverse standardise - gp = GaussianProcess(SKLJL()) + gp = GaussianProcess(GPJL()) emulator3 = Emulator( gp, iopairs, @@ -174,7 +174,7 @@ end constructor_tests(iopairs, Σ, norm_factors, decomposition) # truncation - only test here, where singular value of Σ differ - gp = GaussianProcess(SKLJL()) + gp = GaussianProcess(GPJL()) emulator4 = Emulator( gp, iopairs,

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The data, a vector of moments of the droplet mass -distribution, are obtained by running Cloudy with the parameters set to their -true values. The covariance is obtained from model output. The calibration stage -is performed by an ensemble Kalman inversion (EKI), in which Cloudy has to be -run once per iteration and for each ensemble member. The resulting input-output -pairs ``\{\theta_i, \mathcal{G}(\theta_i)\}_i`` are used to train an emulator -model. This emulator ``\widetilde{\mathcal{G}}(\theta)`` is cheap to evaluate; it replaces the original parameter-to-data map in the Markov chain Monte Carlo (MCMC) sampling, which produces (approximate) samples of the posterior parameter distribution. These samples are the final output of the CES algorithm. - -![Cloudy_overview](../assets/cloudy_ces_schematic.png) +The following schematic gives an overview of the example: + +![cloudy_schematic](../assets/cloudy_ces_schematic_resized.png) + +The input to the CES algorithm consists of data ``y``, the observational covariance ``Γ``, and prior parameter distributions. The data, a vector of moments of the droplet mass distribution, are obtained by running Cloudy with the parameters set to their true values. The covariance is obtained from model output. The calibration stage is performed by an ensemble Kalman inversion (EKI), in which Cloudy has to be run once per iteration and for each ensemble member. The resulting input-output pairs ``\{\theta_i, \mathcal{G}(\theta_i)\}_i`` are used to train an emulator model. This emulator ``\widetilde{\mathcal{G}}(\theta)`` is cheap to evaluate; it replaces the original parameter-to-data map in the Markov chain Monte Carlo (MCMC) sampling, which produces (approximate) samples of the posterior parameter distribution. These samples are the final output of the CES algorithm. [This paper](https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022MS002994) describes Cloudy in much more detail and shows results of experiments using CES to learn model parameters. @@ -91,6 +85,7 @@ using EnsembleKalmanProcesses using EnsembleKalmanProcesses.Observations using EnsembleKalmanProcesses.ParameterDistributions using EnsembleKalmanProcesses.DataContainers +using EnsembleKalmanProcesses.PlotRecipes ``` The module `DynamicalModel.jl` is the forward solver; it provides a function @@ -127,7 +122,9 @@ As we are working with Bayesian methods, we treat the parameters we want to learn as random variables whose prior distributions we specify here. The prior distributions will behave like an "initial guess" for the likely region of parameter space where we expect the solution to be located. -We use `constrained_gaussian` to add the desired scale and bounds to the prior distribution, in particular we place lower bounds to preserve positivity (and numerical stability). +We use `constrained_gaussian` to add the desired scale and bounds to the prior +distribution, in particular we place lower bounds to preserve positivity (and +numerical stability). ```julia # We choose to use normal distributions to represent the prior distributions of @@ -138,6 +135,16 @@ prior_k = constrained_gaussian(param_names[3], 0.2, 1.0, 1e-4, Inf) priors = combine_distributions([prior_N0, prior_θ, prior_k]) ``` +The plot recipe for `ParameterDistribution` types allows for quick visualization of the priors: + +```julia +# Plot the priors +p = plot(priors, constrained=false) +savefig(p, output_directory * "cloudy_priors.png") +``` + +![priors](../assets/cloudy_priors.png) + #### Generate (synthetic) observations We generate synthetic observations by running Cloudy 100 times with the true parameters (i.e., with the true initial Gamma distribution of droplet masses) and then adding noise to simulate measurement error. @@ -225,6 +232,9 @@ particles over subsequent iterations of the optimization, both in the computational (unconstrained) and physical (constrained) spaces. +![eki_iterations_animation](../assets/eki_cloudy.gif) + + ### Walkthrough of the code: `Cloudy_emulate_sample.jl` This file performs the emulation and sampling stages of the CES algorithm. @@ -238,11 +248,10 @@ using Distributions using StatsBase using GaussianProcesses using LinearAlgebra -using StatsPlots -using Plots -using Plots.PlotMeasures using Random using JLD2 +ENV["GKSwstype"] = "100" +using CairoMakie, PairPlots ``` as well as the relevant CES packages needed to construct the emulators and @@ -309,7 +318,7 @@ optimizer_options = Dict( Emulation is performed through the construction of an `Emulator` object from the following components: -* a wrapper for the machine learning tool to be used as emulator +* a wrapper for the machine learning tool (`mlt`) to be used as emulator * the input-output pairs on which the emulator will be trained * optional arguments specifying data processing and dimensionality reduction functionality @@ -321,25 +330,12 @@ gppackage = GPJL() gp_kernel = SE(1.0, 1.0) + Mat52Ard(zeros(3), 0.0) + Noise(log(2.0)) # Wrapper for GP -gaussian_process = GaussianProcess( +mlt = GaussianProcess( gppackage; kernel = gp_kernel, prediction_type = pred_type, noise_learn = false, ) - -# Use all input-output pairs available from the EKI iterations -input_output_pairs = get_training_points(ekiobj, - length(get_u(ekiobj))-1) - -# The data processing normalizes input data, and decorrelates output data with -# information from Γy -emulator = Emulator( - gaussian_process, - input_output_pairs, - obs_noise_cov = Γy, - normalize_inputs = true -) ``` And similarly for `rf-scalar`: @@ -350,14 +346,19 @@ kernel_structure = SeparableKernel( OneDimFactor() ) -srfi = ScalarRandomFeatureInterface( +mlt = ScalarRandomFeatureInterface( n_features, n_params, kernel_structure = kernel_structure, optimizer_options = optimizer_options, ) -retained_svd_frac = 1.0 +``` + +We construct the emulator using all input-output pairs obtained in the +calibration stage, and we want the output data to be decorrelated with information from Γy: + +``` input_output_pairs = get_training_points(ekiobj, length(get_u(ekiobj))-1) @@ -367,14 +368,11 @@ norm_factors = get_standardizing_factors( ) emulator = Emulator( - srfi, - input_output_pairs; + mlt, + input_output_pairs, obs_noise_cov = Γy, - normalize_inputs = true, standardize_outputs = true, standardize_outputs_factors = vcat(norm_factors...), - retained_svd_frac = retained_svd_frac, - decorrelate = true # use SVD to decorrelate outputs ) ``` @@ -413,8 +411,7 @@ The emulator predicts both a mean value and a covariance. The last step is to plug the emulator into an MCMC algorithm, which is then used to produce samples from the posterior distribution of the parameters. Essentially, the emulator acts as a stand-in for the original forward model (which in most cases of interest is computationally expensive to run) during the MCMC sampling process. We use the mean across all parameter ensembles from the EKI as the initial -parameters for the MCMC. Before running the actual MCMC chain, we determine a -good step size: +parameters for the MCMC. Before running the actual MCMC chain, we determine a good step size by running chains of length `N = 2000`: ```julia # initial values @@ -439,8 +436,8 @@ new_step = optimize_stepsize( ) ``` -We choose a sample size of 100'000 for the actual MCMC, discarding the first -1'000 samples as burn-in: +We choose a sample size of 100,000 for the actual MCMC, discarding the first +1,000 samples as burn-in: ```julia # Now begin the actual MCMC @@ -467,17 +464,73 @@ indicating a high-quality estimation. Additionally, visualizing the prior distributions alongside the posteriors shows the distributional change effected by the Bayesian learning process. ### Results -The following three plots show the posterior distributions obtained by the CES -algorithm, for the inverse problem of finding the parameters ``N_{0, -0}``, ``k_0``, and ``\theta_0``, which define a gamma distribution of droplet -masses in Cloudy at time ``t = 0``. The results are shown in the unbounded space -where the CES algorithm takes place. The samples posterior distributions are -shown as grey histograms, the parameters' prior distribution are shown in blue, -and the true parameter values are marked as vertical green lines. - -![posterior_N0_rf](../assets/posterior_rf-scalar_N0.png) -![posterior_theta_rf](../assets/posterior_rf-scalar_theta.png) -![posterior_k_rf](../assets/posterior_rf-scalar_k.png) + +We first produce pair plots (also known as corner plots or scatter plot matrices) to visualize the posterior parameter distributions as a grid of histograms. Recall that the task was to solve the inverse problem of finding the parameters ``N_{0, 0}``, ``k_0``, and ``\theta_0``, which define a gamma distribution of droplet masses in Cloudy at time ``t = 0``. + +```julia +# Make pair plots of the posterior distributions in the unconstrained +# and in the constrained space (this uses `PairPlots.jl`) +figpath_unconstr = joinpath(output_directory, + "joint_posterior_unconstr.png") +figpath_constr = joinpath(output_directory, + "joint_posterior_constr.png") +labels = get_name(posterior) + +data_unconstr = (; [(Symbol(labels[i]), + posterior_samples_unconstr[i, :]) for i in 1:length(labels)]...) +data_constr = (; [(Symbol(labels[i]), + posterior_samples_constr[i, :]) for i in 1:length(labels)]...) + +p_unconstr = pairplot(data_unconstr => (PairPlots.Scatter(),)) +p_constr = pairplot(data_constr => (PairPlots.Scatter(),)) +``` + +For the scalar RF emulator, the results (shown in the constrained/physical space) look as follows: + +![joint_posterior](../assets/joint_posterior_constr_resized.png) + +In addition, we plot the marginals of the posterior distributions: +```julia +for idx in 1:n_params + + # Find the range of the posterior samples + xmin = minimum(posterior_samples_constr[idx, :]) + xmax = maximum(posterior_samples_constr[idx, :]) + + # Create a figure and axis for plotting + fig = Figure(; size = (800, 600)) + ax = Axis(fig[1, 1]) + + # Histogram for posterior samples + hist!(ax, posterior_samples_constr[idx, :], bins = 100, + color = :darkorange, label = "posterior") + + # Plotting the prior distribution + hist!(ax, prior_samples_constr[idx, :], bins = 10000, + color = :slategray) + + # Adding a vertical line for the true value + vlines!(ax, [ϕ_true[idx]], color = :indigo, linewidth = 2.6, + label = "true " * param_names[idx]) + + xlims!(ax, xmin, xmax) + ylims!(ax, 0, Inf) + + # Setting title and labels + ax.title = param_names[idx] + ax.xlabel = "Value" + ax.ylabel = "Density" +``` +This is what the marginal distributions of the three parameters look like, again for the case of scalar RF and plotted in the constrained/physical space: + +![posterior_N0_rf](../assets/posterior_rf-scalar_N0_resized.png) + +![posterior_theta_rf](../assets/posterior_rf-scalar_theta_resized.png) + +![posterior_k_rf](../assets/posterior_rf-scalar_k_resized.png) + +Here, the posterior distributions are shown as orange histograms, the prior distribution are shown as grey histograms (though with the exception of the parmaeter `k`, they are barely visible), and the true parameter values are marked as vertical purple lines. + ### Appendix: What Does Cloudy Do? diff --git a/examples/Cloudy/Manifest.toml b/examples/Cloudy/Manifest.toml deleted file mode 100644 index 9ec1ec910..000000000 --- a/examples/Cloudy/Manifest.toml +++ /dev/null @@ -1,1560 +0,0 @@ -# This file is machine-generated - editing it directly is not advised - -[[AbstractFFTs]] -deps = ["LinearAlgebra"] -git-tree-sha1 = 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03b74a92231c89402d29f8974aa8010247c4cc4e Mon Sep 17 00:00:00 2001 From: Melanie Date: Sun, 3 Dec 2023 23:57:52 -0500 Subject: [PATCH 09/15] Update Cloudy example based on Ollie's comments --- examples/Cloudy/Cloudy_calibrate.jl | 39 +++--- examples/Cloudy/Cloudy_emulate_sample.jl | 158 +++++++++++++---------- examples/Cloudy/DynamicalModel.jl | 10 -- 3 files changed, 110 insertions(+), 97 deletions(-) diff --git a/examples/Cloudy/Cloudy_calibrate.jl b/examples/Cloudy/Cloudy_calibrate.jl index bff90bdff..8171b0b51 100644 --- a/examples/Cloudy/Cloudy_calibrate.jl +++ b/examples/Cloudy/Cloudy_calibrate.jl @@ -1,5 +1,5 @@ # Reference the in-tree version of CalibrateEmulateSample on Julias load path -include(joinpath(@__DIR__, "../..", "ci", "linkfig.jl")) +include(joinpath(@__DIR__, "../", "ci", "linkfig.jl")) # Import modules using Distributions @@ -23,6 +23,7 @@ using EnsembleKalmanProcesses using EnsembleKalmanProcesses.Observations using EnsembleKalmanProcesses.ParameterDistributions using EnsembleKalmanProcesses.DataContainers +using EnsembleKalmanProcesses.PlotRecipes ################################################################################ @@ -31,10 +32,10 @@ using EnsembleKalmanProcesses.DataContainers # # # # # This example uses Cloudy, a microphysics model that simulates the # -# coalescence of cloud droplets into bigger drops, to demonstrate how # -# the full Calibrate-Emulate-Sample pipeline can be used for Bayesian # -# learning and uncertainty quantification of parameters, given some # -# observations. # +# collision and coalescence of cloud droplets into bigger drops, to # +# demonstrate how the full Calibrate-Emulate-Sample pipeline can be # +# used for Bayesian learning and uncertainty quantification of # +# parameters, given some observations. # # # # Specifically, this examples shows how to learn parameters of the # # initial cloud droplet mass distribution, given observations of some # @@ -55,19 +56,14 @@ using EnsembleKalmanProcesses.DataContainers # # ################################################################################ - rng_seed = 41 Random.seed!(rng_seed) rng = Random.seed!(Random.GLOBAL_RNG, rng_seed) homedir = pwd() -figure_save_directory = homedir * "/output/" -data_save_directory = homedir * "/output/" -if ~isdir(figure_save_directory) - mkdir(figure_save_directory) -end -if ~isdir(data_save_directory) - mkdir(data_save_directory) +output_directory = homedir * "/output/" +if ~isdir(output_directory) + mkdir(output_directory) end ### @@ -96,7 +92,9 @@ prior_N0 = constrained_gaussian(param_names[1], 400, 300, 0.4 * N0_true, Inf) prior_θ = constrained_gaussian(param_names[2], 1.0, 5.0, 1e-1, Inf) prior_k = constrained_gaussian(param_names[3], 0.2, 1.0, 1e-4, Inf) priors = combine_distributions([prior_N0, prior_θ, prior_k]) - +# Plot the priors +p = plot(priors, constrained=false) +savefig(p, output_directory * "cloudy_priors.png") ### ### Define the data from which we want to learn the parameters @@ -113,7 +111,6 @@ n_moments = length(moments) # Collision-coalescence kernel to be used in Cloudy tspan = (0.0, 1.0) -print("tspan ", tspan) coalescence_coeff = 1 / 3.14 / 4 / 100 kernel_func = x -> coalescence_coeff kernel = Cloudy.KernelTensors.CoalescenceTensor(kernel_func, 0, 300.0) @@ -189,10 +186,8 @@ println(get_u_mean_final(ekiobj)) u_stored = get_u(ekiobj, return_array = false) g_stored = get_g(ekiobj, return_array = false) -#@save data_save_directory * "parameter_storage_eki.jld2" u_stored -#@save data_save_directory * "data_storage_eki.jld2" g_stored save( - joinpath(data_save_directory, "cloudy_calibrate_results.jld2"), + joinpath(output_directory, "cloudy_calibrate_results.jld2"), "inputs", u_stored, "outputs", @@ -213,7 +208,7 @@ save( gr(size = (1200, 400)) u_init = get_u_prior(ekiobj) -anim_eki_unconst_cloudy = @animate for i in 1:N_iter +anim_eki_unconst_cloudy = @animate for i in 1:(N_iter-1) u_i = get_u(ekiobj, i) p1 = plot(u_i[1, :], u_i[2, :], seriestype = :scatter, @@ -273,11 +268,11 @@ anim_eki_unconst_cloudy = @animate for i in 1:N_iter end gif(anim_eki_unconst_cloudy, - joinpath(figure_save_directory, "eki_unconst_cloudy.gif"), fps = 1) # hide + joinpath(output_directory, "eki_unconst_cloudy.gif"), fps = 1) # hide # Plots in the constrained space ϕ_init = transform_unconstrained_to_constrained(priors, u_init) -anim_eki_cloudy = @animate for i in 1:N_iter +anim_eki_cloudy = @animate for i in 1:(N_iter-1) ϕ_i = get_ϕ(priors, ekiobj, i) p1 = plot(ϕ_i[1, :], ϕ_i[2, :], seriestype = :scatter, @@ -339,4 +334,4 @@ anim_eki_cloudy = @animate for i in 1:N_iter end gif(anim_eki_cloudy, - joinpath(figure_save_directory, "eki_cloudy.gif"), fps = 1) # hide + joinpath(output_directory, "eki_cloudy.gif"), fps = 1) # hide diff --git a/examples/Cloudy/Cloudy_emulate_sample.jl b/examples/Cloudy/Cloudy_emulate_sample.jl index d4cb64aad..d49715b90 100644 --- a/examples/Cloudy/Cloudy_emulate_sample.jl +++ b/examples/Cloudy/Cloudy_emulate_sample.jl @@ -1,16 +1,16 @@ # Reference the in-tree version of CalibrateEmulateSample on Julias load path -include(joinpath(@__DIR__, "../..", "ci", "linkfig.jl")) +include(joinpath(@__DIR__, "../", "ci", "linkfig.jl")) # Import modules using Distributions using StatsBase using GaussianProcesses using LinearAlgebra -using StatsPlots -using Plots -using Plots.PlotMeasures using Random using JLD2 +ENV["GKSwstype"] = "100" +using CairoMakie, PairPlots + # Import Calibrate-Emulate-Sample modules using CalibrateEmulateSample.Emulators @@ -33,10 +33,10 @@ end # # # # # This example uses Cloudy, a microphysics model that simulates the # -# coalescence of cloud droplets into bigger drops, to demonstrate how # -# the full Calibrate-Emulate-Sample pipeline can be used for Bayesian # -# learning and uncertainty quantification of parameters, given some # -# observations. # +# collision and coalescence of cloud droplets into bigger drops, to # +# demonstrate how the full Calibrate-Emulate-Sample pipeline can be # +# used for Bayesian learning and uncertainty quantification of # +# parameters, given some observations. # # # # Specifically, this examples shows how to learn parameters of the # # initial cloud droplet mass distribution, given observations of some # @@ -104,7 +104,7 @@ function main() ] # Specify cases to run (e.g., case_mask = [2] only runs the second case) - case_mask = [1, 2] + case_mask = [2] # These settings are the same for all Gaussian Process cases pred_type = YType() # we want to predict data @@ -119,10 +119,11 @@ function main() "n_iteration" => 20, ) - # We use the same input-output-pairs and normalization factors for + # We use the same input-output-pairs and normalization factors for # Gaussian Process and Random Feature cases input_output_pairs = get_training_points(ekiobj, - length(get_u(ekiobj))-1) norm_factors = get_standardizing_factors(get_outputs(input_output_pairs)) + length(get_u(ekiobj))-1) + norm_factors = get_standardizing_factors(get_outputs(input_output_pairs)) for case in cases[case_mask] println(" ") @@ -136,24 +137,15 @@ function main() # Kernel is the sum of a squared exponential (SE), Matérn 5/2, and # white noise gp_kernel = SE(1.0, 1.0) + Mat52Ard(zeros(3), 0.0) + Noise(log(2.0)) - gaussian_process = GaussianProcess( + + # Define machine learning tool + mlt = GaussianProcess( gppackage; kernel = gp_kernel, prediction_type = pred_type, noise_learn = false, ) - # The data processing normalizes input data, and decorrelates - # output data with information from Γy - emulator = Emulator( - gaussian_process, - input_output_pairs, - obs_noise_cov = Γy, - normalize_inputs = false, - standardize_outputs = true, - standardize_outputs_factors = vcat(norm_factors...), - ) - elseif case == "rf-scalar" kernel_structure = SeparableKernel( @@ -161,31 +153,30 @@ function main() OneDimFactor() ) - srfi = ScalarRandomFeatureInterface( + # Define machine learning tool + mlt = ScalarRandomFeatureInterface( n_features, n_params, kernel_structure = kernel_structure, optimizer_options = optimizer_options, ) - retained_svd_frac = 1.0 - - emulator = Emulator( - srfi, - input_output_pairs; - obs_noise_cov = Γy, - normalize_inputs = true, - standardize_outputs = true, - standardize_outputs_factors = vcat(norm_factors...), - retained_svd_frac = retained_svd_frac, - decorrelate = true # use SVD to decorrelate outputs - ) - else error("Case $case is not implemented yet.") end + # The data processing normalizes input data, and decorrelates + # output data with information from Γy + emulator = Emulator( + mlt, + input_output_pairs, + obs_noise_cov = Γy, + #normalize_inputs = false, + standardize_outputs = true, + standardize_outputs_factors = vcat(norm_factors...), + ) + optimize_hyperparameters!(emulator) # Check how well the emulator predicts on the true parameters @@ -199,7 +190,7 @@ function main() println(vec(y_mean)) println("true data: ") println(truth_sample) # what was used as truth - println("Emulator ($(case)) predicted standard deviation") + println("Emulator ($(case)) predicted standard deviation: ") println(sqrt.(diag(y_var[1], 0))) println("Emulator ($(case)) MSE (truth): ") println(mean((truth_sample - vec(y_mean)) .^ 2)) @@ -248,40 +239,77 @@ function main() println("posterior covariance") println(post_cov) - # Plot the posteriors together with the priors and the true parameter - # values (in the transformed/unconstrained space) + # Prior samples + prior_samples_unconstr = sample(rng, priors, Int(1e4)) + prior_samples_constr = transform_unconstrained_to_constrained( + priors, prior_samples_unconstr) + + # Posterior samples + posterior_samples_unconstr = + vcat([get_distribution(posterior)[name] + for name in get_name(posterior)]...) # samples are columns + posterior_samples_constr = + mapslices(x -> transform_unconstrained_to_constrained(posterior, x), + posterior_samples_unconstr, dims = 1) + + # Make pair plots of the posterior distributions in the unconstrained + # and in the constrained space (this uses `PairPlots.jl`) + figpath_unconstr = joinpath(output_directory, + "joint_posterior_unconstr_" * case * ".png") + figpath_constr = joinpath(output_directory, + "joint_posterior_constr.png_" * case * ".png") + labels = get_name(posterior) + + data_unconstr = (; [(Symbol(labels[i]), + posterior_samples_unconstr[i, :]) for i in 1:length(labels)]...) + data_constr = (; [(Symbol(labels[i]), + posterior_samples_constr[i, :]) for i in 1:length(labels)]...) + + p_unconstr = pairplot(data_unconstr => (PairPlots.Scatter(),)) + p_constr = pairplot(data_constr => (PairPlots.Scatter(),)) + save(figpath_unconstr, p_unconstr) + save(figpath_constr, p_constr) + + # Plot the marginal posterior distributions together with the priors + # and the true parameter values (in the constrained space) n_params = length(get_name(posterior)) - gr(size = (800, 600)) - for idx in 1:n_params - posterior_samples = dropdims( - get_distribution(posterior)[param_names[idx]], dims = 1) # Find the range of the posterior samples - xmin = minimum(posterior_samples) - xmax = maximum(posterior_samples) - xs = collect(range(xmin, stop = xmax, length = 1000)) - - label = "true " * param_names[idx] - histogram( - posterior_samples, - bins = 100, - normed = true, - fill = :slategray, - thickness_scaling = 2.0, - lab = "posterior", - legend = :outertopright, - ) + xmin = minimum(posterior_samples_constr[idx, :]) + xmax = maximum(posterior_samples_constr[idx, :]) + + # Create a figure and axis for plotting + fig = Figure(; size = (800, 600)) + ax = Axis(fig[1, 1]) + + # Histogram for posterior samples + hist!(ax, posterior_samples_constr[idx, :], bins = 100, + color = :darkorange, label = "posterior") + + # Plotting the prior distribution + hist!(ax, prior_samples_constr[idx, :], bins = 10000, + color = :slategray) + + # Adding a vertical line for the true value + vlines!(ax, [ϕ_true[idx]], color = :indigo, linewidth = 2.6, + label = "true " * param_names[idx]) + + xlims!(ax, xmin, xmax) + ylims!(ax, 0, nothing) + + # Setting title and labels + ax.xlabel = "Value" + ax.ylabel = "Density" + ax.title = param_names[idx] + ax.titlesize = 20 - prior_dist = get_distribution(mcmc.prior)[param_names[idx]] - plot!(xs, prior_dist, w = 2.6, color = :blue, lab = "prior") - plot!([θ_true[idx]], seriestype = "vline", w = 2.6, lab = label) - title!(param_names[idx]) + # Save the figure (marginal posterior distribution in constrained + # space) figname = "posterior_" * case * "_" * param_names[idx] * ".png" - figpath = joinpath(output_directory, figname) - StatsPlots.savefig(figpath) - linkfig(figpath) + figpath_marg_constr = joinpath(output_directory, figname) + save(figpath_marg_constr, fig) end end diff --git a/examples/Cloudy/DynamicalModel.jl b/examples/Cloudy/DynamicalModel.jl index 172c85a66..099d47d29 100644 --- a/examples/Cloudy/DynamicalModel.jl +++ b/examples/Cloudy/DynamicalModel.jl @@ -49,18 +49,8 @@ distribution at the end time of the simulation. function run_dyn_model(ϕ::Array{FT, 1}, settings::ModelSettings{FT}) where {FT <: AbstractFloat} # Generate the initial distribution - # TODO: Obviously the GammaPrimitiveParticleDistribution should not be - # hard-coded here. Since update_params has been removed from - # ParticleDistributions.jl, I tried the following: - # Determine the type of the distribution, then create a new instance of - # that type using the desired parameters. This doesn't work; I get an - # error saying LoadError: MethodError: no method matching GammaPrimitiveParticleDistribution{Float64}(::Float64, ::Float64, ::Float64) - - #dist_init_type = typeof(settings.dist) - #dist_init = dist_init_type(ϕ...) dist_init = GammaPrimitiveParticleDistribution(ϕ...) moments_init = get_moments(dist_init) - #dist_init = settings.dist(ϕ...) # Set up ODE problem: dM/dt = f(M, ϕ, t) tspan = (FT(0), FT(1)) From be7821209dda5fdcfdaae672d36d836ff7dc785e Mon Sep 17 00:00:00 2001 From: Melanie Date: Mon, 4 Dec 2023 01:00:03 -0500 Subject: [PATCH 10/15] Finalize --- docs/src/assets/cloudy_ces_schematic.png | Bin 154392 -> 0 bytes .../joint_posterior_constr_gpjl_resized.png | Bin 0 -> 71373 bytes ...nt_posterior_constr_rf-scalar_resized.png} | Bin .../assets/posterior_gp-gpjl_N0_resized.png | Bin 0 -> 19358 bytes .../assets/posterior_gp-gpjl_k_resized.png | Bin 0 -> 19814 bytes .../posterior_gp-gpjl_theta_resized.png | Bin 0 -> 18404 bytes docs/src/assets/posterior_rf-scalar_N0.png | Bin 28757 -> 0 bytes .../assets/posterior_rf-scalar_N0_resized.png | Bin 14377 -> 0 bytes docs/src/assets/posterior_rf-scalar_k.png | Bin 30928 -> 0 bytes .../assets/posterior_rf-scalar_k_resized.png | Bin 19749 -> 0 bytes docs/src/assets/posterior_rf-scalar_theta.png | Bin 29539 -> 0 bytes .../posterior_rf-scalar_theta_resized.png | Bin 12387 -> 0 bytes docs/src/examples/Cloudy_example.md | 21 ++++++++++++------ examples/Cloudy/Cloudy_emulate_sample.jl | 3 +-- 14 files changed, 15 insertions(+), 9 deletions(-) delete mode 100644 docs/src/assets/cloudy_ces_schematic.png create mode 100644 docs/src/assets/joint_posterior_constr_gpjl_resized.png rename docs/src/assets/{joint_posterior_constr_resized.png => joint_posterior_constr_rf-scalar_resized.png} (100%) create mode 100644 docs/src/assets/posterior_gp-gpjl_N0_resized.png create mode 100644 docs/src/assets/posterior_gp-gpjl_k_resized.png create mode 100644 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