Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks

This repository contains the supplementary code to the manuscript here. The codes should be sufficient to reproduce all the results presented.

Dependencies: numpy, scipy, sklearn, torch, matplotlib, seaborn, pandas

Contents

Poisson

• PoissonExample: fully runnable code example for all weighting strategies on the Poisson equation for different modes.
• poisson_adam.py, poisson_rms.py, poisson_ada.py: codes to run inference of poisson solutions for different modes and optimizers as reported in Appendix D.
• EvaluationAdam, EvaluationRMS, EvaluationAdaGrad: evaluate results from poisson_*.py to generate plots from paper

Sobolev

• sobolev.py: run inference on sobolev training example.

Active Turbulence

The training data is publicly available here.

• solve_vort_torus.py, solve_vort_square.py: Infers solution of active turbulence problem in annular and squared domain.
• eval_solve_vort_torus.py, eval_solve_vort_square.py: Evaluation scripts for solution code.
• eval_solve_vort_square_gradient.py: Retrieve backpropagated gradients for solution in squared domain.
• solve_vort_square_convergence_rand.py: Perform convergence study for forward solution.
• inference_pressure_catastrophic.py: Inference of model parameters and effictive pressure with catastrophic interference.
• timing_forward.py, timing_inverse.py: Time comparison for different methods in Appendix C.
• activation_reconstruction.py, activation_evaluation.py: Reconstruction and evaluation of the data under different activation functions as in Appendix C.
• Notebooks produce plots for errors in forward and inverse modeling problems.