From 2e86183682d8e24e87fee4d464fa6b27438a9b45 Mon Sep 17 00:00:00 2001 From: kuanshi <kuanshi@stanford.edu> Date: Mon, 18 Apr 2022 13:19:57 -0700 Subject: [PATCH] kz - adding reference to PLoM example --- Examples/qfem-0022/README.rst | 29 ++++++++++++++++++++++++++++- 1 file changed, 28 insertions(+), 1 deletion(-) diff --git a/Examples/qfem-0022/README.rst b/Examples/qfem-0022/README.rst index 29120cc1..6d504896 100644 --- a/Examples/qfem-0022/README.rst +++ b/Examples/qfem-0022/README.rst @@ -7,6 +7,23 @@ Two-Dimensional Truss: PLoM Modeling and Simulation | Problem files | :github:`Download <Examples/qfem-0022>` | +----------------+------------------------------------------+ +About PLoM +^^^^^^^^^^^^ + +**PLoM** is an open source python package that implements the algorithm of **Probabilistic +Learning on Manifolds** with and without constraints ([SoizeGhanem2016]_, [SoizeGhanem2020]_) +for *generating realizations of a random vector in a finite Euclidean space that are +statistically consistent with a given dataset of that vector*. + +PLoM functionality in SimCenter tools is built upon `PLoM <https://github.com/sanjayg0/PLoM>`_ +package (available under MIT license), an opensource python package for Probabilistic +Learning on Manifolds [ZhongGualGovindjee2021]_. The package mainly consists of python +modules and invokes a dynamic library for more efficiently computing the gradient of +the potential, and can be imported and run on Linux, macOS, and Windows platform. + +Problem Statement +^^^^^^^^^^^^^^^^^^^ + Consider the problem simulating response of a two-dimensional truss structure with uncertain material properties shown in the following figure. The goal of the exercise is to demonstrate the use of ``PLoM model`` method under ``SimCenterUQ``. @@ -96,4 +113,14 @@ page would bring up a dialogue window for saving the model file to a user-define .. figure:: figures/RES4.png :align: center - :figclass: align-center \ No newline at end of file + :figclass: align-center + + +.. [SoizeGhanem2016] + Soize, C., & Ghanem, R. (2016). Data-driven probability concentration and sampling on manifold. Journal of Computational Physics, 321, 242-258. + +.. [SoizeGhanem2020] + Soize, C., & Ghanem, R. (2020). Physicsâconstrained nonâGaussian probabilistic learning on manifolds. International Journal for Numerical Methods in Engineering, 121(1), 110-145. + +.. [ZhongGualGovindjee2021] + Zhong, K., Gual, J., and Govindjee, S., PLoM python package v1.0, https://github.com/sanjayg0/PLoM (2021). \ No newline at end of file