PDEformer-2: a versatile foundation model for two-dimensional partial differential equations

Abstract

Partial differential equations (PDEs) are fundamental to modeling physical systems. Traditional PDE solvers are often computationally expensive. Neural operators require independent training for different PDEs, and tend to be data-greedy when adapted to new scenarios. To this end, we introduce PDEformer-2, a versatile foundation model for solving diverse two-dimensional PDEs. The model receives the PDE form as input through a flexible computational graph representation and outputs solutions that can be queried at any spatio-temporal point. Pretrained on a 40 TB dataset spanning varied equation types, domains, boundary conditions, variable counts, and time dependence, PDEformer-2 enables instant zero-shot predictions for familiar PDEs and adapts faster to unseen ones than specialized baselines, achieving lower errors with limited samples. It also facilitates efficient inverse problem solving, successfully recovering unknown PDE parameters, including scalar coefficients and fields, in experiments.