GNOT: A General Neural Operator Transformer for Operator Learning

TL;DR

GNOT introduces a scalable transformer-based framework for learning PDE solution operators, effectively handling irregular meshes, multiple inputs, and multi-scale problems, with significant improvements over existing methods.

Contribution

The paper presents GNOT, a novel neural operator transformer with a heterogeneous attention layer and geometric gating, enabling flexible and scalable operator learning.

Findings

Achieves significant performance improvements on multiple datasets.

Effectively handles irregular meshes and multiple input functions.

Scales well to large datasets and complex PDEs.

Abstract

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input functions, and complexity of the PDEs' solution. To address these challenges, we propose a general neural operator transformer (GNOT), a scalable and effective transformer-based framework for learning operators. By designing a novel heterogeneous normalized attention layer, our model is highly flexible to handle multiple input functions and irregular meshes. Besides, we introduce a geometric gating mechanism which could be viewed as a soft domain decomposition to solve the multi-scale problems. The large model capacity of the transformer architecture grants our model the possibility to scale to large datasets and practical problems. We conduct extensive experiments on multiple challenging datasets from different domains and achieve a remarkable improvement compared with alternative methods. Our code and data are publicly available at \url{https://github.com/thu-ml/GNOT}.