language:
- en
license: mit
pretty_name: Neural Parametric Solver
task_categories:
- other
tags:
- physics
- physics-informed
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}
}