Introduction

This is a repository containing codes developed for the Minitutorial: "Multi-Modal Data Driven and Physics-Informed Machine Learning with Uncertainty for Materials Applications", presented at the SIAM Conference on Materials Science (MS24) held at Pittsburg from May 19-23 2024.

Setup & Running

All the codes in this repository can be executed through binders. To execute

• Launch the binder:
• Open a terminal and run install.sh with the following command: sh install.sh
• Run the jupyter notebooks

Contents

This repository contains implementations of Bayesian training methods for neural networks, Physics-Informed Neural Networks (PINNs), and several flavors of Deep Operator Networks.

The repository is organized as follows:

• VI_examples contains slides and exercises/code from the first session on variational inference.
  • A complete repository of the PIMA multimodal learning framework may be found at https://github.com/natrask/pima_torch
• Bayesian_examples contains implementations of three Bayesian training methods.
  • Bayesian_MCD.ipynb is an example of Monte Carlo Dropout (MCD).
  • Bayesian_VI.ipynb is an example of Variational Inference (VI).
  • HMC/Bayesian_HMC.ipynb contains an example of Hamiltonian Monte Carlo (HMC).
• DeepONet_examples contains implementations of three flavors of Deep Operator Networks.
  • vanilla/Linear_elasticity.ipynb is a standard Deep Operator Network.
  • pod/POD_Linear_elasticity.ipynb is a Deep Operator Network with the trunk network formed by a Proper Orthogonal Decomposition (POD) basis.
  • bayesian/Bayesian_linear_elasticity.ipynb is a Bayesian implementation of a Deep Operator Network trained using Bayes by Backpropagation algorithm.
• PINN_example implements a Physics-Informed Neural Network (PINN) to solve Burger's equation in 1D.