2ailesB/neural-parametric-solver-datasets

Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methods

This repository provides the datasets used in the paper "Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methods", presented at ICLR 2025.

Project Page | ArXiv | Code

Usage

To use these datasets with the provided code, follow the setup instructions from the official repository:

# Setup
conda create -n neural-parametric-solver python=3.10.11
pip install -e .

# Example: Train a neural solver on the Helmholtz dataset
python3 main.py dataset=helmholtz exp.lr=0.01 model.input_bc=1 model.input_gradtheta=1

PDEs

We provide 9 datasets:

• Helmholtz equation 1d: 4 versions for this PDE with varying difficulties depending on the range of the parameter $\omega$.
  • (0.5, 3): toy
  • (0.5, 10): medium
  • (0.5, 50): hard
  • (-5, 55): used for OOD experiments
• Poisson equation 1d: 2 versions of the Poisson equation:
  • Scalar forcing term
  • Multiscale functional forcing term
• Non-Linear Reaction Diffusion PDE 1d (temporal)
• Advection PDE 1d (temporal): extracted from PDEBench datasets
• Heat 2d (temporal)

Please refer to the paper or code for additional details on the PDEs, parameter ranges, and Dataloaders.

What's inside the datasets

Each dataset provides the PDE trajectory $u$ along with the PDE parameters, forcing terms (if involved), initial conditions (if involved), and boundary conditions (if involved).

The torch Datasets associated class returns the data as a list containing: (params, forcings, ic, bc), position x, solution u, and the index of the trajectory.

Citation

@inproceedings{leboudec2024learning,
  title={Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methods},
  author={Le Boudec, Lise and de Bezenac, Emmanuel and Serrano, Louis and Regueiro-Espino, Ramon Daniel and Yin, Yuan and Gallinari, Patrick},
  booktitle={The Thirteenth International Conference on Learning Representations},
  year={2025}
}