# Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains

arXiv: https://arxiv.org/abs/2505.18781 · HTML: https://mlsanity.com/paper/2505.18781/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2025.

## Built on by (most cited first, 30 of 62)

- [GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer](https://mlsanity.com/paper/2512.20399/) (2025)
- [Transolver-3: Scaling Up Transformer Solvers to Industrial-Scale Geometries](https://mlsanity.com/paper/2602.04940/) (2026)
- [CarBench: A Comprehensive Benchmark for Neural Surrogates on High-Fidelity 3D Car Aerodynamics](https://mlsanity.com/paper/2512.07847/) (2025)
- [GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training](https://mlsanity.com/paper/2602.20399/) (2026)
- [Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs](https://mlsanity.com/paper/2602.02788/) (2026)
- [SMART: Scalable Mesh-free Aerodynamic Simulations from Raw Geometries using a Transformer-based Surrogate Model](https://mlsanity.com/paper/2601.18707/) (2026)
- [Topological Neural Operators](https://mlsanity.com/paper/2606.09806/) (2026)
- [torch-sla: Differentiable Sparse Linear Algebra with Adjoint Solvers and Sparse Tensor Parallelism for PyTorch](https://mlsanity.com/paper/2601.13994/) (2026)
- [Imposing Boundary Conditions on Neural Operators via Learned Function Extensions](https://mlsanity.com/paper/2602.04923/) (2026)
- [Learning, Solving and Optimizing PDEs with TensorGalerkin: an efficient high-performance Galerkin assembly algorithm](https://mlsanity.com/paper/2602.05052/) (2026)
- [ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning](https://mlsanity.com/paper/2602.11626/) (2026)
- [GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations](https://mlsanity.com/paper/2506.13906/) (2025)
- [Efficient Generative Transformer Operators For Million-Point PDEs](https://mlsanity.com/paper/2512.04974/) (2025)
- [Geometric Laplace Neural Operator](https://mlsanity.com/paper/2512.16409/) (2025)
- [Flowers: A Warp Drive for Neural PDE Solvers](https://mlsanity.com/paper/2603.04430/) (2026)
- [Anchored-Branched Steady-state WInd Flow Transformer (AB-SWIFT): a metamodel for 3D atmospheric flow in urban environments](https://mlsanity.com/paper/2603.25635/) (2026)
- [FA-INR: Adaptive Implicit Neural Representations for Interpretable Exploration of Simulation Ensembles](https://mlsanity.com/paper/2506.06858/) (2025)
- [Hybrid operator learning of wave scattering maps in high-contrast media](https://mlsanity.com/paper/2602.11197/) (2026)
- [Neural Shape Operator Surrogates -- Expression Rate Bounds](https://mlsanity.com/paper/2604.18012/) (2026)
- [GRIFDIR: Graph Resolution-Invariant FEM Diffusion Models in Function Spaces over Irregular Domains](https://mlsanity.com/paper/2605.03497/) (2026)
- [A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds](https://mlsanity.com/paper/2605.08436/) (2026)
- [HiLiftAeroML: A High-Fidelity Computational Fluid Dynamics Dataset for High-Lift Aircraft Aerodynamics](https://mlsanity.com/paper/2605.19565/) (2026)
- [Zero-shot generalization of transformer neural operators to larger domains](https://mlsanity.com/paper/2606.14597/) (2026)
- [GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems](https://mlsanity.com/paper/2607.01128/) (2026)
- [Unsupervised Adaptation of PDE Foundation Models](https://mlsanity.com/paper/2608.07053/) (2026)
- [Preconditioned Physics-Informed Neural Operator Training](https://mlsanity.com/paper/2609.36216/) (2026)
- [PIBNet: a Physics-Inspired Boundary Network for Multiple Scattering Simulations](https://mlsanity.com/paper/2512.02049/) (2025)
- [PGOT: A Physics-Geometry Operator Transformer for Complex PDEs](https://mlsanity.com/paper/2512.23192/) (2025)
- [SurgFormer: Scalable Learning of Organ Deformation with Resection Support and Real-Time Inference](https://mlsanity.com/paper/2603.06543/) (2026)
- [Large-Scale 3D Ground-Motion Synthesis with Physics-Inspired Latent Operator Flow Matching](https://mlsanity.com/paper/2603.17403/) (2026)

## Abstract (arXiv)

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to approximate such PDEs, we find that accurate models are not necessarily computationally efficient and vice versa. We address this issue by proposing a geometry aware operator transformer (GAOT) for learning PDEs on arbitrary domains. GAOT combines novel multiscale attentional graph neural operator encoders and decoders, together with geometry embeddings and (vision) transformer processors to accurately map information about the domain and the inputs into a robust approximation of the PDE solution. Multiple innovations in the implementation of GAOT also ensure computational efficiency and scalability. We demonstrate this significant gain in both accuracy and efficiency of GAOT over several baselines on a large number of learning tasks from a diverse set of PDEs, including achieving state of the art performance on three large scale three-dimensional industrial CFD datasets.