Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometries

TL;DR

This work presents Transolver-3, a new member of the Transolver family as a highly scalable framework designed for high-fidelity physics simulations, and introduces two key architectural optimizations: faster slice and deslice by exploiting matrix multiplication associative property and geometry slice tiling to partition the computation of physical states.

Abstract

Deep learning has emerged as a transformative tool for the neural surrogate modeling of partial differential equations (PDEs), known as neural PDE solvers. However, scaling these solvers to industrial-scale geometries with over $10^8$ cells remains a fundamental challenge due to the prohibitive memory complexity of processing high-resolution meshes. We present Transolver-3, a new member of the Transolver family as a highly scalable framework designed for high-fidelity physics simulations. To bridge the gap between limited GPU capacity and the resolution requirements of complex engineering tasks, we introduce two key architectural optimizations: faster slice and deslice by exploiting matrix multiplication associative property and geometry slice tiling to partition the computation of physical states. Combined with an amortized training strategy by learning on random subsets of original high-resolution meshes and a physical state caching technique during inference, Transolver-3 enables high-fidelity field prediction on industrial-scale meshes. Extensive experiments demonstrate that Transolver-3 is capable of handling meshes with over 160 million cells, achieving impressive performance across three challenging simulation benchmarks, including aircraft and automotive design tasks.

Figures (15)

• Figure 1: The maximum mesh sizes handled by Transolver series.
• Figure 2: Geometry scaling at the training phase. (a) Comparison between the original Physics-Attention and its optimized version with faster slice and deslice. For brevity, we omit the diagonal matrix $\mathbf{d}$. (b) Geometry slice tiling partitions the computation of slice weights $\mathbf{w}$ to save memory. (c) Geometry amortized training allows learning on industrial-scale geometries with randomly sampled subsets.
• Figure 3: Decoupled inference of Transolver-3. (a) Physical state caching: global information is aggregated from the high-resolution mesh into cached states. (b) Full mesh decoding: physical fields on mesh coordinates are predicted by interacting with the physical state cache.
• Figure 4: Car and aircraft simulation tasks, focusing on predictions of physical fields on the vehicle surface as well as surround volume.
• Figure 5: Transolver-3 can produce accurate predictions of drag and lift coefficients on the DrivAerML dataset.