PDEFORMER: TOWARDS A FOUNDATION MODEL FOR ONE-DIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS

作     者：Ye, Zhanhong Huang, Xiang Chen, Leheng Liu, Hongsheng Wang, Zidong Dong, Bin 

作者机构：Beijing International Center for Mathematical Research Peking University Beijing China Central Software Institute Huawei Technologies Co. Ltd Hangzhou China Beijing International Center for Mathematical Research The New Cornerstone Science Laboratory Peking University Beijing China Center for Machine Learning Research Peking University Beijing China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Partial differential equations 

摘      要：This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the seamless integration of both symbolic and numerical information inherent in a PDE. A graph Transformer and an implicit neural representation (INR) are employed to generate mesh-free predicted solutions. Following pretraining on data exhibiting a certain level of diversity, our model achieves zero-shot accuracies on benchmark datasets that is comparable to those of specifically trained expert models. Additionally, PDEformer demonstrates promising results in the inverse problem of PDE coefficient recovery. © 2024, CC BY.