Learning PINNs with Integral Losses

This repository contains the code for the "Learning from Integral Losses in Physics Informed Neural Networks" paper.

In short, this paper pinpoints the biased nature of the MSE loss when training PINNs under integro-differntial equations, proposes multiple solution, and extensively benchmarks them on Poisson, Maxwell, and Smoluchowski PDE systems.

Interactive Data Visualization Dashboards

You can check the following interactive dashboards for the ablation studies in the paper.

• The 2-Dimensional Poisson Problem Ablations Dashboard
• The Smoluchowski Problem Ablations Dashboard
• The High-Dimensional Poisson Solutions Visualization Dashboard
• The High-Dimensional Poisson Training Curves Dashboard

Notes:

• These dashboards are standalone files with the data embedded in them, so it may take a few moments for them to load.
• If the dashboard layout was not properly organized, please zoom in/out the web page until a

Technical Information

1. Python Environment: Run make venv in a terminal to setup a virtual environment.

2. Hyper-parameters: The training configuration files, in JSON format, can be found at the configs directory.

3. Running: See ./main.sh for an example bash script running the trainings.

4. Training Code: Check the bspinn/poisson.py, bspinn/smoluchowski.py, and bspinn/maxwell.py files.