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

TL;DR

GeoTransolver addresses surrogate modeling for CAE on irregular geometries by introducing Geometry-Aware Latent Embeddings (GALE) that couple physics-aware self-attention with cross-attention to a persistent geometry/global context $C$ computed via multi-scale ball queries inspired by DoMINO. Implemented in NVIDIA PhysicsNeMo, the method anchors latent computations to domain structure across transformer depth, improving accuracy, robustness to geometry/regime shifts, and data efficiency. Empirical benchmarks on DrivAerML, SHIFT-SUV, and SHIFT-Wing show competitive or superior performance against Domino, Transolver, and AB-UPT, with strong surface/volume field reconstructions and drag/lift predictions. The work demonstrates that geometry-grounded, globally conditioned transformers can serve as scalable, high-fidelity CAE surrogates for complex, irregular domains and nonlinear regimes, with open-source deployment enabling broader adoption and future multi-physics extensions.

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.

Figures (14)

• Figure 1: The GeoTransolver model architecture. The main contributions of GeoTransolver are twofold: first, a geometry- and global-state-aware context projector, to augment input points and encode a sample context. Second, the addition of cross attention in the PhysicsAttention Layer, known here as a Geometry Aware Latent Embedding layer or GALE layer.
• Figure 2: Design trends, Drag and Lift vs Test Designs
• Figure 3: Design trends for Estate, Drag and Lift vs Test Designs
• Figure 4: Design trends for Fastback, Drag and Lift vs Test Designs
• Figure 5: Surface contour comparisons for Estate