<img src=".\pic\logo.png" alt="Logo" width="30" style="vertical-align: middle;">Neural-Solver-Library (NeuralSolver)

NeuralSolver is an open-source library for deep learning researchers, especially for neural PDE solvers.

:triangular_flag_on_post:News (2025.10) We propose FlashBias (NeurIPS 2025) to support fast computation of scientific models. With FlashBias, it is easy to introduce a learnable spatial distance bias into the Transformer for better geometry learning. Check the Transformer_Spatial_Bias model for details. Welcome to try FlashBias and implement your own scientific bias.

:triangular_flag_on_post:News (2025.03) We release the NeuralSolver as a simple and neat code base for benchmarking neural PDE solvers, which is extended from our previous GitHub repository Transolver.

Features

This library currently supports the following benchmarks:

Six Standard Benchmarks from [FNO] and [geo-FNO]
PDEBench [NeurIPS 2022 Track Datasets and Benchmarks] for benchmarking autoregressive tasks
ShapeNet-Car from [TOG 2018] for benchmarking industrial design tasks

<img src=".\pic\task.png" height = "200" alt="" align=center /> Figure 1. Examples of supported PDE-solving tasks.

Supported Neural Solvers

Here is the list of supported neural PDE solvers:

Some vision backbones can be good baselines for tasks in structured geometries:

Swin Transformer - Swin Transformer: Hierarchical Vision Transformer using Shifted Windows [ICCV 2021] [Code]
U-Net - U-Net: Convolutional Networks for Biomedical Image Segmentation [MICCAI 2015] [Code]

Some classical geometric deep models are also included for design tasks:

Graph-UNet - Graph U-Nets [ICML 2019] [Code]
GraphSAGE - Inductive Representation Learning on Large Graphs [NeurIPS 2017] [Code]
PointNet - PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation [CVPR 2017] [Code]

🌟 We have made a great effort to ensure good reproducibility, and are glad to claim that the official results of all the above methods can be completely reproduced (sometimes even better) by this library.

Usage

Install Python 3.8. For convenience, execute the following command.

bash
pip install -r requirements.txt

Prepare Data. You can obtain the data from our previous repository here.
Train and evaluate the model. We provide the experiment scripts for all benchmarks under the folder ./scripts/. You can reproduce the experiment results as follows:

bash
bash ./scripts/StandardBench/airfoil/Transolver.sh

Develop your own model.

Add the model file to the folder ./models. You can follow the ./models/Transolver.py.
Include the newly added model in the model_dict of ./models/model_factory.py.
Create the corresponding scripts under the folder ./scripts, where you can set hyperparameters following the provided scripts of other models.

Citation

If you find this repo useful, please cite our paper.

@inproceedings{wu2024Transolver,
  title={Transolver: A Fast Transformer Solver for PDEs on General Geometries},
  author={Haixu Wu and Huakun Luo and Haowen Wang and Jianmin Wang and Mingsheng Long},
  booktitle={International Conference on Machine Learning},
  year={2024}
}