  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.
