GNOT: A General Neural Operator Transformer for Operator Learning
This work addresses challenges in operator learning for PDEs, which is essential for applications in scientific computing and engineering, though it appears incremental as it builds on existing transformer and neural operator approaches.
The authors tackled the problem of learning solution operators for partial differential equations (PDEs) by proposing GNOT, a transformer-based framework that handles irregular meshes, multiple input functions, and multi-scale problems, achieving a remarkable improvement over alternative methods in experiments across multiple challenging datasets.
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}.