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

Understand

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.