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---
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](https://huggingface.co/papers/2410.06820)", presented at ICLR 2025.
[Project Page](https://2ailesb.github.io/paperpages/neural-solver.html) | [ArXiv](https://arxiv.org/abs/2410.06820) | [Code](https://github.com/2ailesB/neural-parametric-solver)
### Usage
To use these datasets with the provided code, follow the setup instructions from the [official repository](https://github.com/2ailesB/neural-parametric-solver):
```bash
# 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](https://arxiv.org/abs/2410.06820) or [code](https://github.com/2ailesB/neural-parametric-solver) 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](https://github.com/2ailesB/neural-parametric-solver/tree/main/ngd_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
```bibtex
@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}
}
``` |