PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations
CoRR(2024)
摘要
This paper introduces PDEformer, a neural solver for partial differential
equations (PDEs) capable of simultaneously addressing various types of PDEs. We
advocate representing 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 surpass those of
adequately trained expert models. Additionally, PDEformer demonstrates
promising results in the inverse problem of PDE coefficient recovery.
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