PDENNEval: A Comprehensive Evaluation of Neural Network Methods for Solving PDEs

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.