Transolver: A Fast Transformer Solver for PDEs on General Geometries
Haixu Wu Huakun Luo Haowen Wang Jianmin Wang Mingsheng Long
Transformers have empowered many milestones across various fields and have
recently been applied to solve partial differential equations (PDEs). However,
since PDEs are typically discretized into large-scale meshes with complex
geometries, it is challenging for Transformers to capture intricate physical
correlations directly from massive individual points. Going beyond superficial
and unwieldy meshes, we present Transolver based on a more foundational idea,
which is learning intrinsic physical states hidden behind discretized
geometries. Specifically, we propose a new Physics-Attention to adaptively
split the discretized domain into a series of learnable slices of flexible
shapes, where mesh points under similar physical states will be ascribed to the
same slice. By calculating attention to physics-aware tokens encoded from
slices, Transovler can effectively capture intricate physical correlations
under complex geometrics, which also empowers the solver with endogenetic
geometry-general modeling capacity and can be efficiently computed in linear
complexity. Transolver achieves consistent state-of-the-art with 22\% relative
gain across six standard benchmarks and also excels in large-scale industrial
simulations, including car and airfoil designs.