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.
@article{arxiv.2402.12652,
title = {PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations},
author = {Zhanhong Ye and Xiang Huang and Leheng Chen and Hongsheng Liu and Zidong Wang and Bin Dong},
journal= {arXiv preprint arXiv:2402.12652},
year = {2025}
}