PDEformer：面向一维偏微分方程的基础模型
PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations
AI总结：
本文提出PDEformer，一种基于计算图表示、结合图Transformer和隐式神经表示的神经求解器，可处理多种一维PDE，预训练后实现零样本求解并有效解决系数恢复反问题。
摘要：
本文介绍了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。我们提出将PDE表示为计算图的形式，从而促进PDE中固有的符号信息和数值信息的无缝集成。采用图Transformer和隐式神经表示（INR）来生成无网格的预测解。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与专门训练的专家模型相当的零样本准确率。此外，PDEformer在PDE系数恢复的反问题中展现了有前景的结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
