PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations

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

Keywords: partial differential equation (PDE), foundation model, computational graph, implicit neural representation (INR)

TL;DR: We propose to represent the PDE in the form of a computational graph, making our PDEformer model capable of solving various types of PDEs simultaneously.

Abstract: 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.

Submission Number: 22