PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations
<|reference_start|>PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations: 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.<|reference_end|>
@article{ye2024pdeformer:,
    title={PDEformer: Towards a Foundation Model for One-Dimensional Partial
  Differential Equations},
    author={Zhanhong Ye, Xiang Huang, Leheng Chen, Hongsheng Liu, Zidong Wang, Bin
  Dong},
    journal={arXiv preprint arXiv:2402.12652},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.12652},
    primaryClass={math.NA cs.NA}
}