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.

翻译：本文提出PDEformer，一种能够同时处理多种类型偏微分方程（PDE）的神经求解器。我们主张将PDE表示为计算图的形式，从而促进PDE中符号信息与数值信息的无缝融合。采用图Transformer与隐式神经表示（INR）生成无网格预测解。在具有一定多样性的数据上进行预训练后，我们的模型在基准数据集上的零样本精度超过了充分训练的专家模型。此外，PDEformer在PDE系数反演这一逆问题中展现出令人期待的结果。