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Learning partial differential equations' (PDEs) solution operators is anessential problem in machine learning. However, there are several challengesfor learning operators in practical applications like the irregular mesh,multiple input functions, and complexity of the PDEs' solution. To addressthese challenges, we propose a general neural operator transformer (GNOT), ascalable and effective transformer-based framework for learning operators. Bydesigning a novel heterogeneous normalized attention layer, our model is highlyflexible to handle multiple input functions and irregular meshes. Besides, weintroduce a geometric gating mechanism which could be viewed as a soft domaindecomposition to solve the multi-scale problems. The large model capacity ofthe transformer architecture grants our model the possibility to scale to largedatasets and practical problems. We conduct extensive experiments on multiplechallenging datasets from different domains and achieve a remarkableimprovement compared with alternative methods. Our code and data are publiclyavailable at \url{https://github.com/thu-ml/GNOT}.

GNOT: A General Neural Operator Transformer for Operator Learning