GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer

TL;DR

GeoTransolver is a novel multiscale geometry-aware transformer that improves physics-based surrogate modeling on irregular domains by integrating domain geometry and boundary conditions into attention mechanisms, leading to higher accuracy and robustness.

Contribution

It introduces GALE, a physics-aware self-attention mechanism coupled with multi-scale geometry context, enhancing operator learning for complex irregular domains.

Findings

Outperforms existing methods in accuracy and robustness

Demonstrates data efficiency and improved generalization

Provides qualitative insights through contour plots and design trends

Abstract

We present GeoTransolver, a Multiscale Geometry-Aware Physics Attention Transformer for CAE that replaces standard attention with GALE, coupling physics-aware self-attention on learned state slices with cross-attention to a shared geometry/global/boundary-condition context computed from multi-scale ball queries (inspired by DoMINO) and reused in every block. Implemented and released in NVIDIA PhysicsNeMo, GeoTransolver persistently projects geometry, global and boundary condition parameters into physical state spaces to anchor latent computations to domain structure and operating regimes. We benchmark GeoTransolver on DrivAerML, Luminary SHIFT-SUV, and Luminary SHIFT-Wing, comparing against Domino, Transolver (as released in PhysicsNeMo), and literature-reported AB-UPT, and evaluate drag/lift R2 and Relative L1 errors for field variables. GeoTransolver delivers better accuracy, improved robustness to geometry/regime shifts, and favorable data efficiency; we include ablations on DrivAerML and qualitative results such as contour plots and design trends for the best GeoTransolver models. By unifying multiscale geometry-aware context with physics-based attention in a scalable transformer, GeoTransolver advances operator learning for high-fidelity surrogate modeling across complex, irregular domains and non-linear physical regimes.