Neural Green's Functions

Seungwoo Yoo · Kyeongmin Yeo · Jisung Hwang · Minhyuk Sung

KAIST

NeurIPS 2025

TL;DR

We propose Neural Green's Functions, a neural operator tailored for linear PDEs, providing strong generalization across diverse source terms, boundary conditions, and geometries.

We recommend using conda to create a virtual environment and install the required dependencies. You can do this using the provided environment.yaml file.

conda env create -f environment.yml
conda activate ngf

With the ngf environment activated, install PyTorch and other dependencies using the command below. Please note that you may need to adjust the PyTorch and CUDA versions to match your system configuration.

pip install torch==2.5.1 torchvision==0.20.1 torchaudio==2.5.1 --index-url https://download.pytorch.org/whl/cu124
pip install pyg_lib torch_scatter torch_sparse torch_cluster torch_spline_conv -f https://data.pyg.org/whl/torch-2.5.1+cu124.html
pip install transformers==4.47.1

This repository provides the model checkpoints trained on shape categories from the MCB-B dataset, which are used in the main experiments of the paper. The checkpoint files are located under the pretrained_experiments directory. The dataset is hosted on the Hugging Face Hub and is available here.

💡 The dataset is approximately 150 GB in size. Please ensure that you have sufficient disk space before downloading.

After setting up the environment and downloading the dataset and model checkpoints, run the following command to perform inference across the four categories:

bash scripts/run_inference.sh

This script launches inference for all four categories in parallel. Each run outputs the predicted solutions along with a CSV file summarizing the evaluation results.

⚠️ This section is currently under construction. Although the training script is provided, the codebase may be updated in future releases.

We also provide the training script for our model, which can be modified to train on your own dataset. To replicate our training runs, use the following command:

bash scripts/run_train.sh

• Release code for core modules and inference script.
• Release model checkpoints and dataset.
• Finish cleaning up the training code (WIP).

If you find our work useful, please consider citing:

@inproceedings{yoo2025ngf,
  title = {{Neural Green's Functions}},
  author = {Yoo, Seungwoo and Yeo, Kyeongmin and Hwang, Jisung and Sung, Minhyuk},
  booktitle = {NeurIPS},
  year = {2025},
}