FEA Final Project with Machine Learning1-Ciara Woellhof.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Title = Development of a Julia-Based Tool to Aid in Solving a Finite Element Analysis Problem\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m  Activating\u001b[22m\u001b[39m project at `c:\\Users\\Ciara Woellhof\\Downloads`\n"
     ]
    }
   ],
   "source": [
    "import Pkg\n",
    "Pkg.activate(\".\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m registry at `C:\\Users\\Ciara Woellhof\\.julia\\registries\\General.toml`\n",
      "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
      "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `C:\\Users\\Ciara Woellhof\\Downloads\\Project.toml`\n",
      "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `C:\\Users\\Ciara Woellhof\\Downloads\\Manifest.toml`\n",
      "\u001b[92m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n",
      "  17006.1 ms\u001b[33m  ? \u001b[39mGridapODEs\n"
     ]
    }
   ],
   "source": [
    "Pkg.add([\"Plots\",\"LinearAlgebra\",\"Random\",\"DataFrames\",\"Flux\",\"StatsBase\",\"Statistics\",\"MLJ\",\"MLJDecisionTreeInterface\",\"MLJBase\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "using LinearAlgebra\n",
    "using Plots\n",
    "using Random\n",
    "using DataFrames\n",
    "# using Flux\n",
    "# using Flux.Optimisers\n",
    "# using StatsBase\n",
    "# using Statistics\n",
    "using MLJ\n",
    "using MLJDecisionTreeInterface\n",
    "import MLJDecisionTreeInterface\n",
    "import MLJBase: fit!, predict\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mFor silent loading, specify `verbosity=0`. \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "import MLJDecisionTreeInterface ✔\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "MLJDecisionTreeInterface.DecisionTreeRegressor"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the DecisionTreeRegressor from the DecisionTree package\n",
    "DecisionTreeRegressor = @load DecisionTreeRegressor pkg=DecisionTree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeRegressor(\n",
       "  max_depth = -1, \n",
       "  min_samples_leaf = 5, \n",
       "  min_samples_split = 2, \n",
       "  min_purity_increase = 0.0, \n",
       "  n_subfeatures = 0, \n",
       "  post_prune = false, \n",
       "  merge_purity_threshold = 1.0, \n",
       "  feature_importance = :impurity, \n",
       "  rng = TaskLocalRNG())"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the DecisionTreeRegressor from the DecisionTree package\n",
    "model = MLJDecisionTreeInterface.DecisionTreeRegressor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Beam Finite Element Analysis struct for solving beam bending problems\n",
    "\n",
    "struct BeamFEA\n",
    "    length::Float64\n",
    "    num_elements::Int\n",
    "    young_modulus::Float64\n",
    "    moment_inertia::Float64\n",
    "    element_length::Float64\n",
    "\n",
    "    # Constructor\n",
    "    function BeamFEA(length::Float64, num_elements::Int, \n",
    "                     young_modulus::Float64, moment_inertia::Float64)\n",
    "        new(length, num_elements, young_modulus, moment_inertia, \n",
    "            length / num_elements)\n",
    "    end\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "compute_element_stiffness (generic function with 1 method)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# Compute the element stiffness matrix for a beam element\n",
    "\n",
    "# Arguments\n",
    "# beam: BeamFEA struct containing beam properties\n",
    "\n",
    "function compute_element_stiffness(beam::BeamFEA)\n",
    "    L = beam.element_length\n",
    "    EI = beam.young_modulus * beam.moment_inertia\n",
    "\n",
    "    # 4x4 element stiffness matrix for Euler-Bernoulli beam\n",
    "    k = [\n",
    "        12/L^3     6/L^2    -12/L^3    6/L^2;\n",
    "        6/L^2      4/L      -6/L^2     2/L;\n",
    "        -12/L^3   -6/L^2    12/L^3    -6/L^2;\n",
    "        6/L^2      2/L      -6/L^2     4/L\n",
    "    ] * EI\n",
    "\n",
    "    return k\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "assemble_global_stiffness (generic function with 1 method)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# Assemble global stiffness matrix for the beam\n",
    "\n",
    "# Arguments\n",
    "# beam: BeamFEA struct\n",
    "\n",
    "function assemble_global_stiffness(beam::BeamFEA)\n",
    "    # Total degrees of freedom\n",
    "    total_dof = 2 * (beam.num_elements + 1)\n",
    "    K = zeros(total_dof, total_dof)\n",
    "    \n",
    "    # Get element stiffness matrix\n",
    "    k_element = compute_element_stiffness(beam)\n",
    "    \n",
    "    # Assembly process\n",
    "    for i in 1:beam.num_elements\n",
    "        # Map local DOFs to global\n",
    "        idx = [2*i-1, 2*i, 2*i+1, 2*i+2]\n",
    "        \n",
    "        # Add element stiffness to global matrix\n",
    "        K[idx, idx] += k_element\n",
    "    end\n",
    "    \n",
    "    return K\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "solve_beam_deflection (generic function with 1 method)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# Solve beam deflection problem\n",
    "\n",
    "# Arguments\n",
    "# beam: BeamFEA struct\n",
    "# force_magnitude: Applied force at the free end\n",
    "\n",
    "function solve_beam_deflection(beam::BeamFEA, force_magnitude::Float64)\n",
    "    # Assemble global stiffness matrix\n",
    "    K = assemble_global_stiffness(beam)\n",
    "    \n",
    "    # Create force vector\n",
    "    total_dof = 2 * (beam.num_elements + 1)\n",
    "    F = zeros(total_dof)\n",
    "    F[end] = force_magnitude\n",
    "    \n",
    "    # Apply fixed-free boundary conditions\n",
    "    # Constrain first two DOFs (fixed end)\n",
    "    K[1, :] .= 0\n",
    "    K[:, 1] .= 0\n",
    "    K[2, :] .= 0\n",
    "    K[:, 2] .= 0\n",
    "    \n",
    "    K[1, 1] = 1\n",
    "    K[2, 2] = 1\n",
    "    \n",
    "    # Solve for displacements\n",
    "    displacement = K \\ F\n",
    "    \n",
    "    return displacement\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "visualize_beam_deformation (generic function with 1 method)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# Create detailed visualization of beam deformation\n",
    "\n",
    "# Arguments\n",
    "# beam: BeamFEA struct\n",
    "# displacement: Displacement vector\n",
    "# force_magnitude: Applied force for annotation\n",
    "\n",
    "function visualize_beam_deformation(beam::BeamFEA, displacement::Vector{Float64}, force_magnitude::Float64)\n",
    "    # Extract y-direction displacements\n",
    "    y_displacements = displacement[2:2:end]\n",
    "    \n",
    "    # Create x-coordinates for undeformed and deformed beam\n",
    "    x_undeformed = range(0, beam.length, length=beam.num_elements+1)\n",
    "    x_deformed = [x_undeformed[i] + y_displacements[i] for i in 1:length(x_undeformed)]\n",
    "    \n",
    "    # Create plot with undeformed and deformed beam\n",
    "    p = plot(layout = @layout[a b], size=(1200, 500), \n",
    "             legend=:topleft, title=\"Beam Deformation Visualization\")\n",
    "    \n",
    "    # Undeformed beam plot\n",
    "    plot!(p[1], x_undeformed, zeros(length(x_undeformed)), \n",
    "          linewidth=3, color=:blue, label=\"Undeformed Beam\",\n",
    "          title=\"Undeformed Beam\", \n",
    "          xlabel=\"Beam Length (m)\", \n",
    "          ylabel=\"Vertical Position (m)\")\n",
    "    scatter!(p[1], x_undeformed, zeros(length(x_undeformed)), \n",
    "             color=:red, label=\"Nodes\")\n",
    "    \n",
    "    # Deformed beam plot\n",
    "    plot!(p[2], x_deformed, y_displacements, \n",
    "          linewidth=3, color=:red, label=\"Deformed Beam\",\n",
    "          title=\"Beam Deflection\", \n",
    "          xlabel=\"Deformed Beam Position (m)\", \n",
    "          ylabel=\"Deflection (m)\")\n",
    "    scatter!(p[2], x_deformed, y_displacements, \n",
    "             color=:blue, label=\"Deformed Nodes\")\n",
    "    \n",
    "    # Annotations\n",
    "    max_deflection = maximum(abs.(y_displacements))\n",
    "    max_deflection_location = x_deformed[argmax(abs.(y_displacements))]\n",
    "    \n",
    "    annotate!(p[2], max_deflection_location, max_deflection, \n",
    "              text(\"Max Deflection: $(round(max_deflection, digits=4)) m\", \n",
    "                   :left, :bottom))\n",
    "    \n",
    "    # Add force annotation to the deformed beam plot\n",
    "    annotate!(p[2], beam.length, 0, \n",
    "              text(\"Applied Force: $(round(force_magnitude, digits=1)) N\", \n",
    "                   :right, :bottom))\n",
    "    \n",
    "    display(p)\n",
    "    return p\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "simulate_data (generic function with 1 method)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simulate data for training the machine learning model\n",
    "function simulate_data(num_samples::Int)\n",
    "    data = []\n",
    "    for _ in 1:num_samples\n",
    "        beam_length = rand(1.0:0.1:5.0)      # meters\n",
    "        num_elements = rand(5:1:50)          # elements\n",
    "        young_modulus = rand(50e9:1e9:300e9) # Pa\n",
    "        moment_inertia = rand(1e-6:1e-6:1e-3) # m^4\n",
    "        force = rand(100.0:100.0:5000.0)     # Newtons\n",
    "\n",
    "        beam = BeamFEA(beam_length, num_elements, young_modulus, moment_inertia)\n",
    "        displacements = solve_beam_deflection(beam, force)\n",
    "        max_deflection = maximum(abs.(displacements[2:2:end]))\n",
    "\n",
    "        push!(data, (beam_length, num_elements, young_modulus, moment_inertia, force, max_deflection))\n",
    "    end\n",
    "    return data\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "partition_data (generic function with 2 methods)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Function to partition data into training and test sets\n",
    "function partition_data(features, target, train_ratio=0.8)\n",
    "    n = length(target)\n",
    "    idx = shuffle(1:n)\n",
    "    train_size = Int(floor(train_ratio * n))\n",
    "    \n",
    "    train_idx = idx[1:train_size]\n",
    "    test_idx = idx[train_size+1:end]\n",
    "    \n",
    "    X_train = features[train_idx, :]\n",
    "    y_train = target[train_idx]\n",
    "    X_test = features[test_idx, :]\n",
    "    y_test = target[test_idx]\n",
    "    \n",
    "    return X_train, y_train, X_test, y_test\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000-element Vector{Any}:\n",
       " (4.0, 23, 1.77e11, 8.5e-5, 400.0, 0.00010634762379526284)\n",
       " (4.0, 15, 1.65e11, 0.000211, 500.0, 5.744650294404516e-5)\n",
       " (1.3, 35, 1.37e11, 0.000738, 900.0, 1.1572013530621529e-5)\n",
       " (2.5, 5, 2.53e11, 3.8e-5, 200.0, 5.200748907842729e-5)\n",
       " (1.5, 25, 1.31e11, 0.000506, 1900.0, 4.299550432951178e-5)\n",
       " (4.4, 24, 8.1e10, 0.000672, 4000.0, 0.0003233392122254894)\n",
       " (1.2, 21, 2.67e11, 0.000263, 4900.0, 8.373563463968402e-5)\n",
       " (1.5, 18, 1.58e11, 0.000576, 4100.0, 6.757647679333923e-5)\n",
       " (4.8, 44, 1.35e11, 0.000247, 900.0, 0.00012955465587759934)\n",
       " (4.1, 6, 2.31e11, 0.000739, 1100.0, 2.6419228043044035e-5)\n",
       " (2.1, 16, 2.78e11, 0.000337, 1100.0, 2.4656832397572103e-5)\n",
       " (4.4, 50, 2.89e11, 0.000468, 4700.0, 0.00015289977228675079)\n",
       " (4.0, 38, 2.05e11, 4.2e-5, 2500.0, 0.001161440185825284)\n",
       " ⋮\n",
       " (1.2, 23, 2.86e11, 0.00032, 900.0, 1.18006993006842e-5)\n",
       " (2.8, 11, 9.8e10, 1.6e-5, 2200.0, 0.0039285714285735756)\n",
       " (4.8, 40, 7.1e10, 0.000255, 3100.0, 0.0008218724109336785)\n",
       " (1.7, 41, 1.08e11, 0.000618, 3700.0, 9.424068080804083e-5)\n",
       " (1.7, 48, 2.88e11, 0.000573, 4500.0, 4.635689354689213e-5)\n",
       " (3.0, 43, 1.29e11, 0.000655, 2800.0, 9.94141665157128e-5)\n",
       " (2.4, 5, 2.27e11, 0.000261, 2200.0, 8.91184363765278e-5)\n",
       " (1.7, 48, 2.43e11, 0.000311, 3400.0, 7.648234157879046e-5)\n",
       " (1.5, 11, 2.61e11, 0.000756, 1600.0, 1.2163230554035328e-5)\n",
       " (1.4, 41, 2.79e11, 0.000918, 2900.0, 1.5851820616959694e-5)\n",
       " (1.3, 40, 2.19e11, 0.000925, 2800.0, 1.796865358602709e-5)\n",
       " (2.5, 39, 1.74e11, 0.000381, 4500.0, 0.00016969861525816026)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate synthetic dataset\n",
    "num_samples = 1000\n",
    "data = simulate_data(num_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><div style = \"float: left;\"><span>1000×6 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">975 rows omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">beam_length</th><th style = \"text-align: left;\">num_elements</th><th style = \"text-align: left;\">young_modulus</th><th style = \"text-align: left;\">moment_inertia</th><th style = \"text-align: left;\">force</th><th style = \"text-align: left;\">max_deflection</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">23</td><td style = \"text-align: right;\">1.77e11</td><td style = \"text-align: right;\">8.5e-5</td><td style = \"text-align: right;\">400.0</td><td style = \"text-align: right;\">0.000106348</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">15</td><td style = \"text-align: right;\">1.65e11</td><td style = \"text-align: right;\">0.000211</td><td style = \"text-align: right;\">500.0</td><td style = \"text-align: right;\">5.74465e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: right;\">1.3</td><td style = \"text-align: right;\">35</td><td style = \"text-align: right;\">1.37e11</td><td style = \"text-align: right;\">0.000738</td><td style = \"text-align: right;\">900.0</td><td style = \"text-align: right;\">1.1572e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: right;\">2.5</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">2.53e11</td><td style = \"text-align: right;\">3.8e-5</td><td style = \"text-align: right;\">200.0</td><td style = \"text-align: right;\">5.20075e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: right;\">1.5</td><td style = \"text-align: right;\">25</td><td style = \"text-align: right;\">1.31e11</td><td style = \"text-align: right;\">0.000506</td><td style = \"text-align: right;\">1900.0</td><td style = \"text-align: right;\">4.29955e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">6</td><td style = \"text-align: right;\">4.4</td><td style = \"text-align: right;\">24</td><td style = \"text-align: right;\">8.1e10</td><td style = \"text-align: right;\">0.000672</td><td style = \"text-align: right;\">4000.0</td><td style = \"text-align: right;\">0.000323339</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">7</td><td style = \"text-align: right;\">1.2</td><td style = \"text-align: right;\">21</td><td style = \"text-align: right;\">2.67e11</td><td style = \"text-align: right;\">0.000263</td><td style = \"text-align: right;\">4900.0</td><td style = \"text-align: right;\">8.37356e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">8</td><td style = \"text-align: right;\">1.5</td><td style = \"text-align: right;\">18</td><td style = \"text-align: right;\">1.58e11</td><td style = \"text-align: right;\">0.000576</td><td style = \"text-align: right;\">4100.0</td><td style = \"text-align: right;\">6.75765e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">9</td><td style = \"text-align: right;\">4.8</td><td style = \"text-align: right;\">44</td><td style = \"text-align: right;\">1.35e11</td><td style = \"text-align: right;\">0.000247</td><td style = \"text-align: right;\">900.0</td><td style = \"text-align: right;\">0.000129555</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">10</td><td style = \"text-align: right;\">4.1</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">2.31e11</td><td style = \"text-align: right;\">0.000739</td><td style = \"text-align: right;\">1100.0</td><td style = \"text-align: right;\">2.64192e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">11</td><td style = \"text-align: right;\">2.1</td><td style = \"text-align: right;\">16</td><td style = \"text-align: right;\">2.78e11</td><td style = \"text-align: right;\">0.000337</td><td style = \"text-align: right;\">1100.0</td><td style = \"text-align: right;\">2.46568e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">12</td><td style = \"text-align: right;\">4.4</td><td style = \"text-align: right;\">50</td><td style = \"text-align: right;\">2.89e11</td><td style = \"text-align: right;\">0.000468</td><td style = \"text-align: right;\">4700.0</td><td style = \"text-align: right;\">0.0001529</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">13</td><td style = \"text-align: right;\">4.0</td><td style = \"text-align: right;\">38</td><td style = \"text-align: right;\">2.05e11</td><td style = \"text-align: right;\">4.2e-5</td><td style = \"text-align: right;\">2500.0</td><td style = \"text-align: right;\">0.00116144</td></tr><tr><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td><td style = \"text-align: right;\">&vellip;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">989</td><td style = \"text-align: right;\">1.2</td><td style = \"text-align: right;\">23</td><td style = \"text-align: right;\">2.86e11</td><td style = \"text-align: right;\">0.00032</td><td style = \"text-align: right;\">900.0</td><td style = \"text-align: right;\">1.18007e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">990</td><td style = \"text-align: right;\">2.8</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">9.8e10</td><td style = \"text-align: right;\">1.6e-5</td><td style = \"text-align: right;\">2200.0</td><td style = \"text-align: right;\">0.00392857</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">991</td><td style = \"text-align: right;\">4.8</td><td style = \"text-align: right;\">40</td><td style = \"text-align: right;\">7.1e10</td><td style = \"text-align: right;\">0.000255</td><td style = \"text-align: right;\">3100.0</td><td style = \"text-align: right;\">0.000821872</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">992</td><td style = \"text-align: right;\">1.7</td><td style = \"text-align: right;\">41</td><td style = \"text-align: right;\">1.08e11</td><td style = \"text-align: right;\">0.000618</td><td style = \"text-align: right;\">3700.0</td><td style = \"text-align: right;\">9.42407e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">993</td><td style = \"text-align: right;\">1.7</td><td style = \"text-align: right;\">48</td><td style = \"text-align: right;\">2.88e11</td><td style = \"text-align: right;\">0.000573</td><td style = \"text-align: right;\">4500.0</td><td style = \"text-align: right;\">4.63569e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">994</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">43</td><td style = \"text-align: right;\">1.29e11</td><td style = \"text-align: right;\">0.000655</td><td style = \"text-align: right;\">2800.0</td><td style = \"text-align: right;\">9.94142e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">995</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">2.27e11</td><td style = \"text-align: right;\">0.000261</td><td style = \"text-align: right;\">2200.0</td><td style = \"text-align: right;\">8.91184e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">996</td><td style = \"text-align: right;\">1.7</td><td style = \"text-align: right;\">48</td><td style = \"text-align: right;\">2.43e11</td><td style = \"text-align: right;\">0.000311</td><td style = \"text-align: right;\">3400.0</td><td style = \"text-align: right;\">7.64823e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">997</td><td style = \"text-align: right;\">1.5</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">2.61e11</td><td style = \"text-align: right;\">0.000756</td><td style = \"text-align: right;\">1600.0</td><td style = \"text-align: right;\">1.21632e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">998</td><td style = \"text-align: right;\">1.4</td><td style = \"text-align: right;\">41</td><td style = \"text-align: right;\">2.79e11</td><td style = \"text-align: right;\">0.000918</td><td style = \"text-align: right;\">2900.0</td><td style = \"text-align: right;\">1.58518e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">999</td><td style = \"text-align: right;\">1.3</td><td style = \"text-align: right;\">40</td><td style = \"text-align: right;\">2.19e11</td><td style = \"text-align: right;\">0.000925</td><td style = \"text-align: right;\">2800.0</td><td style = \"text-align: right;\">1.79687e-5</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1000</td><td style = \"text-align: right;\">2.5</td><td style = \"text-align: right;\">39</td><td style = \"text-align: right;\">1.74e11</td><td style = \"text-align: right;\">0.000381</td><td style = \"text-align: right;\">4500.0</td><td style = \"text-align: right;\">0.000169699</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cccccc}\n",
       "\t& beam\\_length & num\\_elements & young\\_modulus & moment\\_inertia & force & max\\_deflection\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Int64 & Float64 & Float64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 4.0 & 23 & 1.77e11 & 8.5e-5 & 400.0 & 0.000106348 \\\\\n",
       "\t2 & 4.0 & 15 & 1.65e11 & 0.000211 & 500.0 & 5.74465e-5 \\\\\n",
       "\t3 & 1.3 & 35 & 1.37e11 & 0.000738 & 900.0 & 1.1572e-5 \\\\\n",
       "\t4 & 2.5 & 5 & 2.53e11 & 3.8e-5 & 200.0 & 5.20075e-5 \\\\\n",
       "\t5 & 1.5 & 25 & 1.31e11 & 0.000506 & 1900.0 & 4.29955e-5 \\\\\n",
       "\t6 & 4.4 & 24 & 8.1e10 & 0.000672 & 4000.0 & 0.000323339 \\\\\n",
       "\t7 & 1.2 & 21 & 2.67e11 & 0.000263 & 4900.0 & 8.37356e-5 \\\\\n",
       "\t8 & 1.5 & 18 & 1.58e11 & 0.000576 & 4100.0 & 6.75765e-5 \\\\\n",
       "\t9 & 4.8 & 44 & 1.35e11 & 0.000247 & 900.0 & 0.000129555 \\\\\n",
       "\t10 & 4.1 & 6 & 2.31e11 & 0.000739 & 1100.0 & 2.64192e-5 \\\\\n",
       "\t11 & 2.1 & 16 & 2.78e11 & 0.000337 & 1100.0 & 2.46568e-5 \\\\\n",
       "\t12 & 4.4 & 50 & 2.89e11 & 0.000468 & 4700.0 & 0.0001529 \\\\\n",
       "\t13 & 4.0 & 38 & 2.05e11 & 4.2e-5 & 2500.0 & 0.00116144 \\\\\n",
       "\t14 & 1.1 & 33 & 2.73e11 & 0.000298 & 2800.0 & 3.78592e-5 \\\\\n",
       "\t15 & 4.7 & 50 & 7.3e10 & 0.00017 & 4000.0 & 0.00151491 \\\\\n",
       "\t16 & 4.7 & 34 & 2.58e11 & 0.000124 & 4000.0 & 0.000587647 \\\\\n",
       "\t17 & 1.0 & 10 & 8.4e10 & 0.000697 & 3500.0 & 5.978e-5 \\\\\n",
       "\t18 & 1.7 & 45 & 1.91e11 & 0.000124 & 4300.0 & 0.000308647 \\\\\n",
       "\t19 & 1.7 & 23 & 1.82e11 & 0.000387 & 2300.0 & 5.5513e-5 \\\\\n",
       "\t20 & 3.6 & 32 & 9.4e10 & 5.9e-5 & 5000.0 & 0.00324558 \\\\\n",
       "\t21 & 2.6 & 39 & 1.57e11 & 0.00016 & 900.0 & 9.31529e-5 \\\\\n",
       "\t22 & 4.5 & 47 & 6.0e10 & 0.000715 & 2800.0 & 0.000293706 \\\\\n",
       "\t23 & 2.7 & 18 & 2.69e11 & 0.000998 & 2400.0 & 2.41375e-5 \\\\\n",
       "\t24 & 4.7 & 41 & 1.64e11 & 0.000881 & 3700.0 & 0.000120359 \\\\\n",
       "\t25 & 1.3 & 36 & 8.9e10 & 0.000318 & 400.0 & 1.83733e-5 \\\\\n",
       "\t26 & 4.0 & 8 & 2.81e11 & 0.0009 & 3600.0 & 5.69395e-5 \\\\\n",
       "\t27 & 1.4 & 28 & 1.96e11 & 0.000462 & 1700.0 & 2.62832e-5 \\\\\n",
       "\t28 & 3.3 & 7 & 1.65e11 & 0.000365 & 1700.0 & 9.31507e-5 \\\\\n",
       "\t29 & 4.0 & 26 & 1.76e11 & 0.000494 & 2100.0 & 9.66139e-5 \\\\\n",
       "\t30 & 4.5 & 33 & 2.0e11 & 0.000542 & 800.0 & 3.32103e-5 \\\\\n",
       "\t$\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ & $\\dots$ \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m1000×6 DataFrame\u001b[0m\n",
       "\u001b[1m  Row \u001b[0m│\u001b[1m beam_length \u001b[0m\u001b[1m num_elements \u001b[0m\u001b[1m young_modulus \u001b[0m\u001b[1m moment_inertia \u001b[0m\u001b[1m force   \u001b[0m\u001b[1m max\u001b[0m ⋯\n",
       "      │\u001b[90m Float64     \u001b[0m\u001b[90m Int64        \u001b[0m\u001b[90m Float64       \u001b[0m\u001b[90m Float64        \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Flo\u001b[0m ⋯\n",
       "──────┼─────────────────────────────────────────────────────────────────────────\n",
       "    1 │         4.0            23        1.77e11        8.5e-5      400.0      ⋯\n",
       "    2 │         4.0            15        1.65e11        0.000211    500.0\n",
       "    3 │         1.3            35        1.37e11        0.000738    900.0\n",
       "    4 │         2.5             5        2.53e11        3.8e-5      200.0\n",
       "    5 │         1.5            25        1.31e11        0.000506   1900.0      ⋯\n",
       "    6 │         4.4            24        8.1e10         0.000672   4000.0\n",
       "    7 │         1.2            21        2.67e11        0.000263   4900.0\n",
       "    8 │         1.5            18        1.58e11        0.000576   4100.0\n",
       "    9 │         4.8            44        1.35e11        0.000247    900.0      ⋯\n",
       "   10 │         4.1             6        2.31e11        0.000739   1100.0\n",
       "   11 │         2.1            16        2.78e11        0.000337   1100.0\n",
       "  ⋮   │      ⋮            ⋮              ⋮              ⋮            ⋮         ⋱\n",
       "  991 │         4.8            40        7.1e10         0.000255   3100.0\n",
       "  992 │         1.7            41        1.08e11        0.000618   3700.0      ⋯\n",
       "  993 │         1.7            48        2.88e11        0.000573   4500.0\n",
       "  994 │         3.0            43        1.29e11        0.000655   2800.0\n",
       "  995 │         2.4             5        2.27e11        0.000261   2200.0\n",
       "  996 │         1.7            48        2.43e11        0.000311   3400.0      ⋯\n",
       "  997 │         1.5            11        2.61e11        0.000756   1600.0\n",
       "  998 │         1.4            41        2.79e11        0.000918   2900.0\n",
       "  999 │         1.3            40        2.19e11        0.000925   2800.0\n",
       " 1000 │         2.5            39        1.74e11        0.000381   4500.0      ⋯\n",
       "\u001b[36m                                                   1 column and 979 rows omitted\u001b[0m"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create DataFrame from the simulated data\n",
    "df = DataFrame(data, [:beam_length, :num_elements, :young_modulus, :moment_inertia, :force, :max_deflection])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000-element Vector{Float64}:\n",
       " 0.00010634762379526284\n",
       " 5.744650294404516e-5\n",
       " 1.1572013530621529e-5\n",
       " 5.200748907842729e-5\n",
       " 4.299550432951178e-5\n",
       " 0.0003233392122254894\n",
       " 8.373563463968402e-5\n",
       " 6.757647679333923e-5\n",
       " 0.00012955465587759934\n",
       " 2.6419228043044035e-5\n",
       " 2.4656832397572103e-5\n",
       " 0.00015289977228675079\n",
       " 0.001161440185825284\n",
       " ⋮\n",
       " 1.18006993006842e-5\n",
       " 0.0039285714285735756\n",
       " 0.0008218724109336785\n",
       " 9.424068080804083e-5\n",
       " 4.635689354689213e-5\n",
       " 9.94141665157128e-5\n",
       " 8.91184363765278e-5\n",
       " 7.648234157879046e-5\n",
       " 1.2163230554035328e-5\n",
       " 1.5851820616959694e-5\n",
       " 1.796865358602709e-5\n",
       " 0.00016969861525816026"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define features and target\n",
    "features = select(df, Not(:max_deflection))\n",
    "target = df.max_deflection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(\u001b[1m800×5 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m beam_length \u001b[0m\u001b[1m num_elements \u001b[0m\u001b[1m young_modulus \u001b[0m\u001b[1m moment_inertia \u001b[0m\u001b[1m force   \u001b[0m\n",
       "     │\u001b[90m Float64     \u001b[0m\u001b[90m Int64        \u001b[0m\u001b[90m Float64       \u001b[0m\u001b[90m Float64        \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────────────\n",
       "   1 │         1.7            23        1.82e11        0.000387   2300.0\n",
       "   2 │         2.6            42        2.57e11        0.000391    100.0\n",
       "   3 │         4.7            40        1.7e11         0.00023     400.0\n",
       "   4 │         1.4            21        2.89e11        0.000873   4300.0\n",
       "   5 │         3.4            48        2.37e11        0.000955    600.0\n",
       "   6 │         3.7             8        1.94e11        0.000379   1500.0\n",
       "   7 │         1.8             8        2.86e11        0.000453   3800.0\n",
       "   8 │         1.6            36        2.06e11        0.000722   1100.0\n",
       "   9 │         3.6            26        2.78e11        0.000384   4000.0\n",
       "  10 │         4.1            38        2.85e11        0.000854   3300.0\n",
       "  11 │         3.8            27        1.61e11        0.000184   4100.0\n",
       "  ⋮  │      ⋮            ⋮              ⋮              ⋮            ⋮\n",
       " 791 │         3.2            33        7.6e10         0.000144   4200.0\n",
       " 792 │         4.4            17        2.57e11        0.000985    700.0\n",
       " 793 │         2.3            29        2.18e11        1.9e-5     4100.0\n",
       " 794 │         3.2            49        9.2e10         0.000898   2000.0\n",
       " 795 │         3.3            42        1.1e11         0.00094    1800.0\n",
       " 796 │         2.6            34        6.7e10         0.000971   4600.0\n",
       " 797 │         3.9             6        2.67e11        0.000712    600.0\n",
       " 798 │         4.0            23        1.77e11        8.5e-5      400.0\n",
       " 799 │         2.0            21        1.0e11         0.000328   1400.0\n",
       " 800 │         1.7            48        2.67e11        0.000776   4000.0\n",
       "\u001b[36m                                                         779 rows omitted\u001b[0m, [5.551296249007058e-5, 2.5873993649977445e-6, 4.8081841431550794e-5, 2.3860767270262142e-5, 9.013188415833533e-6, 7.548350243453485e-5, 5.2794887231976936e-5, 1.1833364709959592e-5, 0.00013489208633129572, 5.558979415882459e-5  …  0.0012280701754413359, 1.216693989607579e-5, 0.0022766779333821996, 7.74668345111378e-5, 5.7446808516630754e-5, 0.00018383878752359096, 1.2309051887387592e-5, 0.00010634762379526284, 8.536585365823378e-5, 3.281979999301241e-5], \u001b[1m200×5 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m beam_length \u001b[0m\u001b[1m num_elements \u001b[0m\u001b[1m young_modulus \u001b[0m\u001b[1m moment_inertia \u001b[0m\u001b[1m force   \u001b[0m\n",
       "     │\u001b[90m Float64     \u001b[0m\u001b[90m Int64        \u001b[0m\u001b[90m Float64       \u001b[0m\u001b[90m Float64        \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼───────────────────────────────────────────────────────────────────\n",
       "   1 │         4.9            37        1.81e11        0.000228   3400.0\n",
       "   2 │         4.6            15        2.89e11        0.000501   3000.0\n",
       "   3 │         1.8            10        2.98e11        0.000342    900.0\n",
       "   4 │         4.1            20        2.15e11        0.000813   2000.0\n",
       "   5 │         2.7            23        2.47e11        0.000757    100.0\n",
       "   6 │         3.9            13        1.3e11         0.000595   4400.0\n",
       "   7 │         2.3            47        8.3e10         0.000423   1900.0\n",
       "   8 │         4.9             8        6.1e10         6.4e-5     2500.0\n",
       "   9 │         1.5            20        1.88e11        8.2e-5     4500.0\n",
       "  10 │         4.7            41        1.64e11        0.000881   3700.0\n",
       "  11 │         4.8            30        2.15e11        0.000939   1000.0\n",
       "  ⋮  │      ⋮            ⋮              ⋮              ⋮            ⋮\n",
       " 191 │         3.3            15        1.38e11        0.000877   3400.0\n",
       " 192 │         2.1            20        9.7e10         0.000123    700.0\n",
       " 193 │         2.7            35        1.78e11        0.000144   4700.0\n",
       " 194 │         1.2            21        2.67e11        0.000263   4900.0\n",
       " 195 │         4.2            21        1.28e11        0.000895    200.0\n",
       " 196 │         1.7            24        1.0e11         0.000544   2300.0\n",
       " 197 │         3.9            14        1.46e11        6.1e-5     1600.0\n",
       " 198 │         3.4            23        2.99e11        0.000347   5000.0\n",
       " 199 │         3.6             8        2.7e11         0.000323   3800.0\n",
       " 200 │         2.2            39        1.13e11        0.000182   1000.0\n",
       "\u001b[36m                                                         179 rows omitted\u001b[0m, [0.0004037026267220903, 9.531110788788332e-5, 1.5895443306247254e-5, 4.69120970277867e-5, 1.4440124292108713e-6, 0.00022184873949601804, 0.00012446950924093871, 0.0031378073770501475, 0.0004378567721832889, 0.00012035934775236686  …  9.270735213900326e-5, 0.000123208448579141, 0.0004950842696635387, 8.373563463968402e-5, 7.332402234614738e-6, 7.187499999982436e-5, 0.0007006512463520185, 0.00016385068383360657, 0.0001568627450980322, 0.00010697267334756064])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Split data into training and test sets\n",
    "X_train, y_train, X_test, y_test = partition_data(features, target, 0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mTraining machine(DecisionTreeRegressor(max_depth = -1, …), …).\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "trained Machine; caches model-specific representations of data\n",
       "  model: DecisionTreeRegressor(max_depth = -1, …)\n",
       "  args: \n",
       "    1:\tSource @522 ⏎ Table{Union{AbstractVector{Continuous}, AbstractVector{Count}}}\n",
       "    2:\tSource @883 ⏎ AbstractVector{Continuous}\n"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train a machine learning model\n",
    "mach = machine(model, X_train, y_train)\n",
    "fit!(mach)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root Mean Squared Error: 0.0014711544494896112\n"
     ]
    }
   ],
   "source": [
    "# Predict on the test set\n",
    "y_pred = predict(mach, X_test)\n",
    "rms = sqrt(mean((y_test .- y_pred).^2))\n",
    "println(\"Root Mean Squared Error: $rms\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "predict_max_deflection (generic function with 1 method)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Function to predict maximum deflection using the trained model\n",
    "function predict_max_deflection(beam_length::Float64, num_elements::Int, \n",
    "    young_modulus::Float64, moment_inertia::Float64, \n",
    "    force::Float64, model)\n",
    "new_data = DataFrame(beam_length=beam_length, num_elements=num_elements, \n",
    "young_modulus=young_modulus, moment_inertia=moment_inertia, \n",
    "force=force)\n",
    "max_deflection_pred = predict(model, new_data)\n",
    "return max_deflection_pred\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "main (generic function with 1 method)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Main function to demonstrate beam FEA with ML prediction\n",
    "function main()\n",
    "    beam_length = 2.0      # meters\n",
    "    num_elements = 20      # elements\n",
    "    young_modulus = 200e9  # Pa (steel)\n",
    "    moment_inertia = 1e-4  # m^4\n",
    "    force = 2000.0         # Newtons\n",
    "    \n",
    "    beam = BeamFEA(beam_length, num_elements, young_modulus, moment_inertia)\n",
    "    displacements = solve_beam_deflection(beam, force)\n",
    "    visualize_beam_deformation(beam, displacements, force)\n",
    "    \n",
    "    max_deflection = maximum(abs.(displacements[2:2:end]))\n",
    "    println(\"Maximum deflection (FEA): \", max_deflection, \" meters\")\n",
    "    \n",
    "    max_deflection_pred = predict_max_deflection(beam_length, num_elements, young_modulus, moment_inertia, force, mach)\n",
    "    println(\"Predicted maximum deflection (ML): \", max_deflection_pred, \" meters\")\n",
    "    \n",
    "    return displacements\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum deflection (FEA): 0.0002000000000007121 meters\n",
      "Predicted maximum deflection (ML): [0.0001418721652767736] meters\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "42-element Vector{Float64}:\n",
       " 0.0\n",
       " 0.0\n",
       " 5.000000000036178e-7\n",
       " 1.0000000000071863e-5\n",
       " 2.0000000000140916e-6\n",
       " 2.000000000013712e-5\n",
       " 4.500000000030948e-6\n",
       " 3.0000000000199518e-5\n",
       " 8.000000000053891e-6\n",
       " 4.0000000000258857e-5\n",
       " 1.2500000000082664e-5\n",
       " 5.00000000003161e-5\n",
       " 1.8000000000117135e-5\n",
       " ⋮\n",
       " 0.00011250000000063203\n",
       " 0.00015000000000069762\n",
       " 0.0001280000000007021\n",
       " 0.00016000000000070306\n",
       " 0.00014450000000077262\n",
       " 0.0001700000000007073\n",
       " 0.00016200000000084357\n",
       " 0.0001800000000007113\n",
       " 0.00018050000000091476\n",
       " 0.00019000000000071222\n",
       " 0.000200000000000986\n",
       " 0.0002000000000007121"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "main()"
   ]
  }
 ],
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