Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

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.

In many real-world applications, such as car and aircraft design, engineers need to simulate how pressure behaves around complex 3D shapes. Traditionally, these simulations can take hours or even days to complete, as they rely on solving complex mathematical equations. In this paper, we present Transolver++, a powerful AI model that significantly accelerates this process while maintaining high accuracy. Through careful optimization, Transolver++ can handle highly detailed 3D geometries with millions of data points, making it practical for real industrial applications. Once trained, it can simulate new scenarios in under a second, delivering a substantial improvement in speed and efficiency. This advancement marks a major step toward replacing traditional simulation tools with AI-powered solutions in engineering and design.