Abstract:While Transformers have demonstrated remarkable potential in modeling Partial Differential Equations (PDEs), modeling large-scale unstructured meshes with complex geometries remains a significant challenge. Existing efficient architectures often employ feature dimensionality reduction strategies, which inadvertently induces Geometric Aliasing, resulting in the loss of critical physical boundary information. To address this, we propose the Physics-Geometry Operator Transformer (PGOT), designed to reconstruct physical feature learning through explicit geometry awareness. Specifically, we propose Spectrum-Preserving Geometric Attention (SpecGeo-Attention). Utilizing a ``physics slicing-geometry injection" mechanism, this module incorporates multi-scale geometric encodings to explicitly preserve multi-scale geometric features while maintaining linear computational complexity $O(N)$. Furthermore, PGOT dynamically routes computations to low-order linear paths for smooth regions and high-order non-linear paths for shock waves and discontinuities based on spatial coordinates, enabling spatially adaptive and high-precision physical field modeling. PGOT achieves consistent state-of-the-art performance across four standard benchmarks and excels in large-scale industrial tasks including airfoil and car designs.
| Comments: | 24 pages, 17 figures |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2512.23192 [cs.LG] |
| (or arXiv:2512.23192v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2512.23192 arXiv-issued DOI via DataCite |
From: Zhuo Zhang [view email]
[v1]
Mon, 29 Dec 2025 04:05:01 UTC (41,454 KB)
[v2]
Tue, 20 Jan 2026 14:33:39 UTC (42,959 KB)
[v3]
Wed, 29 Apr 2026 13:58:01 UTC (34,940 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。