README.md

---
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}
}
```