# Geometry-Aware Anisotropic Boundary Correction for Aerodynamic Simulation

arXiv: https://arxiv.org/abs/2606.09963 · HTML: https://mlsanity.com/paper/2606.09963/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 40 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 19 of 19)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs](https://mlsanity.com/paper/2403.12553/) (2024)
- [AB-UPT: Scaling Neural CFD Surrogates for High-Fidelity Automotive Aerodynamics Simulations via Anchored-Branched Universal Physics Transformers](https://mlsanity.com/paper/2502.09692/) (2025)
- [Continuum Attention for Neural Operators](https://mlsanity.com/paper/2406.06486/) (2024)
- [BENO: Boundary-embedded Neural Operators for Elliptic PDEs](https://mlsanity.com/paper/2401.09323/) (2024)
- [Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulations](https://mlsanity.com/paper/2407.19916/) (2024)
- [Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulations](https://mlsanity.com/paper/2505.14704/) (2025)
- [Temporal Neural Operator for Modeling Time-Dependent Physical Phenomena](https://mlsanity.com/paper/2504.20249/) (2025)
- [Cross-Field Interface-Aware Neural Operators for Multiphase Flow Simulation](https://mlsanity.com/paper/2511.08625/) (2025)

## Abstract (arXiv)

Aerodynamic simulation is a key component of engineering shape design, where core quantities such as the surface pressure coefficient strongly depend on flow dynamics near solid boundaries. Neural operators provide an efficient alternative to expensive Computational Fluid Dynamics (CFD) solvers. However, conventional methods treat the boundary region isotropically, failing to account for the distinct physical behaviors along the boundaries. In reality, the aerodynamic process exhibits anisotropy: along the tangential direction, flow propagates along the wall; along the normal direction, physical quantities are constrained by the wall. To explicitly model the distinct physical behaviors, we propose GeoABC, a geometry-conditioned anisotropic boundary correction framework. GeoABC leverages the boundary geometries to introduce direction-aware boundary correction into the intermediate representations of neural operators, transforming boundary geometry from static input features into a structural prior that modulates physical prediction. On 2D airfoil and 3D car tasks, GeoABC consistently adapts to multiple neural operator backbones, reducing near-boundary relative L2 error by ~38% on average, narrowing the structural near-wall gap shared by mainstream neural operators, and advancing neural operators toward high-fidelity aerodynamic simulation.