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.

翻译：本文介绍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。我们提出以计算图的形式表示PDE，从而促进PDE中符号与数值信息无缝融合。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实现了零样本精度，其性能与经过专门训练的专业模型相当。此外，PDEformer在PDE系数反演问题中展现出令人满意的结果。