Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries
This work addresses the challenge of applying neural PDE solvers to real industrial applications involving complex geometries, representing an incremental advancement over prior methods.
The paper tackles the problem of scaling neural PDE solvers to million-scale geometries required for industrial simulations, achieving a 13% relative improvement on standard benchmarks and over 20% performance gain in high-fidelity industrial simulations with sizes 100 times larger than previous benchmarks.
Although deep models have been widely explored in solving partial differential equations (PDEs), previous works are primarily limited to data only with up to tens of thousands of mesh points, far from the million-point scale required by industrial simulations that involve complex geometries. In the spirit of advancing neural PDE solvers to real industrial applications, we present Transolver++, a highly parallel and efficient neural solver that can accurately solve PDEs on million-scale geometries. Building upon previous advancements in solving PDEs by learning physical states via Transolver, Transolver++ is further equipped with an extremely optimized parallelism framework and a local adaptive mechanism to efficiently capture eidetic physical states from massive mesh points, successfully tackling the thorny challenges in computation and physics learning when scaling up input mesh size. Transolver++ increases the single-GPU input capacity to million-scale points for the first time and is capable of continuously scaling input size in linear complexity by increasing GPUs. Experimentally, Transolver++ yields 13% relative promotion across six standard PDE benchmarks and achieves over 20% performance gain in million-scale high-fidelity industrial simulations, whose sizes are 100$\times$ larger than previous benchmarks, covering car and 3D aircraft designs.