Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains

TL;DR

This paper introduces GAOT, a geometry-aware transformer model that efficiently and accurately learns PDE solutions on arbitrary domains, outperforming existing methods in accuracy and computational efficiency.

Contribution

The paper presents a novel geometry-aware operator transformer with multiscale graph neural encoders and decoders, improving PDE solution approximation on arbitrary domains.

Findings

GAOT achieves state-of-the-art accuracy on 3D CFD datasets.

GAOT demonstrates significant efficiency gains over baseline models.

The model effectively captures complex domain geometries for PDE solutions.

Abstract

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to approximate such PDEs, we find that accurate models are not necessarily computationally efficient and vice versa. We address this issue by proposing a geometry aware operator transformer (GAOT) for learning PDEs on arbitrary domains. GAOT combines novel multiscale attentional graph neural operator encoders and decoders, together with geometry embeddings and (vision) transformer processors to accurately map information about the domain and the inputs into a robust approximation of the PDE solution. Multiple innovations in the implementation of GAOT also ensure computational efficiency and scalability. We demonstrate this significant gain in both accuracy and efficiency of GAOT over several baselines on a large number of learning tasks from a diverse set of PDEs, including achieving state of the art performance on three large scale three-dimensional industrial CFD datasets.