PGOT: Transformer for Complex PDEs with Geometry Awareness
Published:Dec 29, 2025 04:05
•1 min read
•ArXiv
Analysis
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.
Key Takeaways
Reference
“PGOT achieves consistent state-of-the-art performance across four standard benchmarks and excels in large-scale industrial tasks including airfoil and car designs.”