PGOT: Transformer for Complex PDEs with Geometry Awareness

This paper introduces PGOT, a novel Transformer architecture designed to improve PDE modeling, particularly for complex geometries and large-scale unstructured meshes. The core innovation lies in its Spectrum-Preserving Geometric Attention (SpecGeo-Attention) module, which explicitly incorporates geometric information to avoid geometric aliasing and preserve critical boundary information. The spatially adaptive computation routing further enhances the model's ability to handle both smooth regions and shock waves. The consistent state-of-the-art performance across benchmarks and success in industrial tasks highlight the practical significance of this work.