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

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arxiv 2402.12652 v3 pith:J5LBSLXG submitted 2024-02-20 math.NA cs.NA

Zhanhong Ye , Xiang Huang , Leheng Chen , Hongsheng Liu , Zidong Wang , Bin Dong This is my paper · ORCID
classification math.NAcs.NA
keywords pdeformerdifferentialequationsgraphmodelneuralpartialpdes
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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.

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Cited by 5 Pith papers

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    A domain-decomposition subspace neural network method solves linear and nonlinear PDEs with errors down to 1e-13 and lower training cost than PINN, DGM, DRM, and LocELM on 1D/2D benchmarks.

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