mlsanityData to 14 Oct 2026

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

arXiv 2512.20399 ↗First posted 23 Dec 2025cs.LG physics.comp-phcited by 23

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Abstract (arXiv)

We present GeoTransolver, a multiscale geometry-aware physics attention transformer for Computer Aided Engineering (CAE). GeoTransolver extends the Transolver backbone with GALE (Geometry-Aware Latent Embeddings) attention, which pairs physics-aware self-attention on learned state slices with cross-attention to a shared geometry and global context computed via multi-scale ball queries (inspired by Domino) and reused in every block. Implemented and released in NVIDIA PhysicsNeMo, GeoTransolver persistently projects geometry and global parameters, into physical state spaces to anchor computations to domain structure and operating regimes. We benchmark on DrivAerML, SHIFT-SUV, and SHIFT-Wing against Domino, Transolver (PhysicsNeMo implementation), and literature-reported AB-UPT, evaluating drag/lift R2 and relative L1 errors on field variables. As an additional nonlinear structural mechanics application, we also report Transolver and GeoTransolver results on bumper-beam and full-vehicle Body-in-White (BIW) crash-dynamics benchmarks, evaluating relative L2 trajectory error and probe-level kinematic MSE. GeoTransolver delivers improved accuracy, robustness to geometry and regime shifts, and favorable data efficiency; we include DrivAerML ablations and qualitative contour and design-trend results, advancing operator learning for high-fidelity surrogates on complex, irregular, non-linear domains.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 36 of its 57 references that are in the map. First posted on arXiv 23 Dec 2025.

Builds on

36 of 57 references.

References · 36

  1. 2017Attention Is All You Needcited by 60,361
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  3. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  4. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  5. 2021E(n) Equivariant Graph Neural Networkscited by 965
  6. 2020Learning Mesh-Based Simulation with Graph Networkscited by 868
  7. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  8. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  9. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 427
  10. 2019Machine Learning for Fluid Mechanicscited by 385
  11. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 349
  12. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 336
24 more
  1. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 326
  2. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 264
  3. 2021Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformerscited by 248
  4. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  5. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  6. 2022MultiScale MeshGraphNetscited by 98
  7. 2025AdaMuon: Adaptive Muon Optimizercited by 67
  8. 2025Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domainscited by 62
  9. 2025AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformerscited by 53
  10. 2024DrivAerML: High-Fidelity Computational Fluid Dynamics Dataset for Road-Car External Aerodynamicscited by 35
  11. 2024Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularitycited by 34
  12. 2023ViTO: Vision Transformer-Operatorcited by 29
  13. 2025DoMINO: A Decomposable Multi-scale Iterative Neural Operator for Modeling Large Scale Engineering Simulationscited by 27
  14. 2024HAMLET: Graph Transformer Neural Operator for Partial Differential Equationscited by 24
  15. 2024X-MeshGraphNet: Scalable Multi-Scale Graph Neural Networks for Physics Simulationcited by 22
  16. 2025Factorized Implicit Global Convolution for Automotive Computational Fluid Dynamics Predictioncited by 20
  17. 2025TripNet: Learning Large-scale High-fidelity 3D Car Aerodynamics with Triplane Networkscited by 14
  18. 2020Multiresolution Convolutional Autoencoderscited by 10
  19. 2022A composable machine-learning approach for steady-state simulations on high-resolution gridscited by 8
  20. 2025Geometry-Informed Neural Operator Transformercited by 8
  21. 2022Learning time-dependent PDE solver using Message Passing Graph Neural Networkscited by 7
  22. 2025FLARE: Fast Low-rank Attention Routing Enginecited by 6
  23. 2025AB-UPT for Automotive and Aerospace Applicationscited by 5
  24. 2025A Benchmarking Framework for AI models in Automotive Aerodynamicscited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 23.

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  1. 2026AeroJEPA: Learning Semantic Latent Representations for Scalable 3D Aerodynamic Field Modelingcited by 4
  2. 2026High-Fidelity Industrial Crash Dynamics Prediction via Geometry-Aware Operator Learning with Memory-Efficient Low-Rank Attentioncited by 4
  3. 2026RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamicscited by 1
  4. 2026ShardTensor: Domain Parallelism for Scientific Machine Learningcited by 1
  5. 2026Crash Assessment via Mesh-Based Graph Neural Networks and Physics-Aware Attentioncited by 1
  6. 2026HiLiftAeroML: A High-Fidelity Computational Fluid Dynamics Dataset for High-Lift Aircraft Aerodynamicscited by 1
  7. 2026Adapting Automotive Aerodynamics Surrogates to New Vehicle Families via Transfer Learningcited by 1
  8. 2026CarCrashNet: A Large-Scale Dataset and Hierarchical Neural Solver for Data-Driven Structural Crash Simulationcited by 0
  9. 2026Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decompositioncited by 0
  10. 2026Attention mechanism for scalable mesh-based neural surrogates of free-surface fluidscited by 0
  11. 2026Uncertainty Quantification for AI-Driven Crash Simulation Surrogates: A Comparative Study of Monte Carlo Dropout and Deep Ensemble on Open-Source Bumper Beam Benchmarkcited by 0
  12. 2026Physics Transformer: Tailoring Transformer for General PDE Predictioncited by 0
11 more
  1. 2026Read, Write, Relax: Why Neural PDE Surrogates Need Both Global and Local Processingcited by 0
  2. 2026KPI-Conditioned Generative Design of Automotive Hood Inner Panels: A Two-Stage Retrieval-Generation Pipeline with Surrogate-Based Performance Estimationcited by 0
  3. 2026PhysicsBench: A Unified Leaderboard for Generative and Predictive Models in Engineering Design and Simulationcited by 0
  4. 2026A Data Fusion Framework for Grounding Aerospace Surrogate Model via Experimental Wind-Tunnel Observationscited by 0
  5. 2026Distance-Aware Attention and Wall-Distance Expert Routing for Transformer-Based 3D Flow Predictioncited by 0
  6. 2026Predictive Uncertainty for Neural CAE Surrogatescited by 0
  7. 2026Does Transolver really need a Transformer?cited by 0
  8. 2026D-JEPA: Design-Recoverable JEPA Representation with Swappable Physics Decoderscited by 0
  9. 2026SHIFT-Truck: A High-Fidelity Aerodynamics Dataset and Benchmark for Pickup Truckscited by 0
  10. 2026Threshold-Aware Conformal Routingcited by 0
  11. 2026Geometry Meets Physics: Data-Efficient Pre-Training for Unstructured Neural PDE Solverscited by 0