PDENNEval: A Comprehensive Evaluation of Neural Network Methods for Solving PDEs
Ping Wei, Menghan Liu, Jianhuan Cen, Ziyang Zhou, Liao Chen, Qingsong Zou
Abstract
The rapid development of neural network (NN) methods for solving partial differential equations (PDEs) has created an urgent need for evaluation and comparison of these methods. In this study, we propose PDENNEval, a comprehensive and systematic evaluation of 12 NN methods for PDEs. These methods are classified into function learning type and operator learning type based on their different mathematical foundations. The evaluation is implemented using a diverse dataset comprising 19 distinct PDE problems selected from various scientific fields such as fluid, materials, finance, and electromagnetic. Several evaluation results are reported, aiming to provide guidance for further research in this field. Our code and data are publicly available at https://github.com/zhouzy36/PDENNEval.
BibTeX
@inproceedings{ijcai2024p573,
title = {PDENNEval: A Comprehensive Evaluation of Neural Network Methods for Solving PDEs},
author = {Wei, Ping and Liu, Menghan and Cen, Jianhuan and Zhou, Ziyang and Chen, Liao and Zou, Qingsong},
booktitle = {Proceedings of the Thirty-Third International Joint Conference on
Artificial Intelligence, {IJCAI-24}},
publisher = {International Joint Conferences on Artificial Intelligence Organization},
editor = {Kate Larson},
pages = {5181--5189},
year = {2024},
month = {8},
note = {Main Track},
doi = {10.24963/ijcai.2024/573},
url = {https://doi.org/10.24963/ijcai.2024/573},
}