Transolver: A Fast Transformer Solver for PDEs on General Geometries

Transolver: A Fast Transformer Solver for PDEs on General Geometries

2024 | Haixu Wu, Huakun Luo, Haowen Wang, Jianmin Wang, Mingsheng Long
Transolver is a fast transformer solver for partial differential equations (PDEs) on general geometries. It addresses the challenge of capturing intricate physical correlations from massive mesh points by learning intrinsic physical states hidden behind discretized geometries. The method introduces Physics-Attention, which adaptively splits the discretized domain into learnable slices of flexible shapes, grouping mesh points with similar physical states into the same slice. By applying attention to physics-aware tokens encoded from these slices, Transolver effectively captures complex physical correlations under complex geometries, achieving linear complexity in computation. It excels in six standard benchmarks with a 22% relative gain and performs well in large-scale industrial simulations, including car and airfoil designs. The model is efficient, scalable, and generalizable to out-of-distribution scenarios. Transolver replaces the standard attention mechanism with Physics-Attention, enabling it to focus on physical states rather than mesh points, thus improving performance in handling complex geometries and multiphysics interactions. The method is validated through extensive experiments on various benchmarks and practical design tasks, demonstrating its effectiveness in solving PDEs on general geometries.Transolver is a fast transformer solver for partial differential equations (PDEs) on general geometries. It addresses the challenge of capturing intricate physical correlations from massive mesh points by learning intrinsic physical states hidden behind discretized geometries. The method introduces Physics-Attention, which adaptively splits the discretized domain into learnable slices of flexible shapes, grouping mesh points with similar physical states into the same slice. By applying attention to physics-aware tokens encoded from these slices, Transolver effectively captures complex physical correlations under complex geometries, achieving linear complexity in computation. It excels in six standard benchmarks with a 22% relative gain and performs well in large-scale industrial simulations, including car and airfoil designs. The model is efficient, scalable, and generalizable to out-of-distribution scenarios. Transolver replaces the standard attention mechanism with Physics-Attention, enabling it to focus on physical states rather than mesh points, thus improving performance in handling complex geometries and multiphysics interactions. The method is validated through extensive experiments on various benchmarks and practical design tasks, demonstrating its effectiveness in solving PDEs on general geometries.
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[slides and audio] Transolver%3A A Fast Transformer Solver for PDEs on General Geometries