# Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulations

arXiv: https://arxiv.org/abs/2407.19916 · HTML: https://mlsanity.com/paper/2407.19916/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 67 references that are in the map.
- First posted on arXiv 29 Jul 2024.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Learned Initializations for Optimizing Coordinate-Based Neural Representations](https://mlsanity.com/paper/2012.02189/) (2020)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [Towards Sparse Hierarchical Graph Classifiers](https://mlsanity.com/paper/1811.01287/) (2018)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Operator Learning with Neural Fields: Tackling PDEs on General Geometries](https://mlsanity.com/paper/2306.07266/) (2023)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)
- [Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries](https://mlsanity.com/paper/2403.14788/) (2024)
- [Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows](https://mlsanity.com/paper/2109.01514/) (2021)
- [Geodesic Convolutional Shape Optimization](https://mlsanity.com/paper/1802.04016/) (2018)
- [SMT 2.0: A Surrogate Modeling Toolbox with a focus on Hierarchical and Mixed Variables Gaussian Processes](https://mlsanity.com/paper/2305.13998/) (2023)
- [Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flows](https://mlsanity.com/paper/1907.09909/) (2019)
- [PINs: Progressive Implicit Networks for Multi-Scale Neural Representations](https://mlsanity.com/paper/2202.04713/) (2022)

## Built on by (most cited first, 24 of 24)

- [BlendedNet: A Blended Wing Body Aircraft Dataset and Surrogate Model for Aerodynamic Predictions](https://mlsanity.com/paper/2509.07209/) (2025)
- [TripNet: Learning Large-scale High-fidelity 3D Car Aerodynamics with Triplane Networks](https://mlsanity.com/paper/2503.17400/) (2025)
- [Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulations](https://mlsanity.com/paper/2505.14704/) (2025)
- [Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations](https://mlsanity.com/paper/2504.18591/) (2025)
- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometries](https://mlsanity.com/paper/2504.02459/) (2025)
- [AeroJEPA: Learning Semantic Latent Representations for Scalable 3D Aerodynamic Field Modeling](https://mlsanity.com/paper/2605.05586/) (2026)
- [SuperWing: a comprehensive transonic wing dataset for data-driven aerodynamic design](https://mlsanity.com/paper/2512.14397/) (2025)
- [FA-INR: Adaptive Implicit Neural Representations for Interpretable Exploration of Simulation Ensembles](https://mlsanity.com/paper/2506.06858/) (2025)
- [NeurIPS 2024 ML4CFD Competition: Results and Retrospective Analysis](https://mlsanity.com/paper/2506.08516/) (2025)
- [BlendedNet++: A dataset and benchmark for field-resolved aerodynamics and inverse design of blended wing body aircraft](https://mlsanity.com/paper/2512.03280/) (2025)
- [A Geometry-Aware Triplane Field Network for Vehicle Aerodynamic Prediction](https://mlsanity.com/paper/2606.07724/) (2026)
- [GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems](https://mlsanity.com/paper/2607.01128/) (2026)
- [PLAID: A Unified Data Model for Machine Learning on Heterogeneous Physics Simulations](https://mlsanity.com/paper/2505.02974/) (2025)
- [Physics-based machine learning for mantle convection simulations](https://mlsanity.com/paper/2505.16041/) (2025)
- [Computational Fluid Dynamics Optimization of F1 Front Wing using Physics Informed Neural Networks](https://mlsanity.com/paper/2509.01963/) (2025)
- [A Multi-fidelity Double-Delta Wing Dataset and Empirical Scaling Laws for GNN-based Aerodynamic Field Surrogate](https://mlsanity.com/paper/2512.20941/) (2025)
- [Signal-Aware Conditional Diffusion Surrogates for Transonic Wing Pressure Prediction](https://mlsanity.com/paper/2604.11263/) (2026)
- [APIC: Amortized Physics-Informed Calibration using Neural Processes](https://mlsanity.com/paper/2606.03355/) (2026)
- [Geometry-Aware Anisotropic Boundary Correction for Aerodynamic Simulation](https://mlsanity.com/paper/2606.09963/) (2026)
- [CoFINN: Conservation Flux Informed Neural Networks for Physics Problems Governed by Conservation Laws](https://mlsanity.com/paper/2607.06587/) (2026)
- [Spatio-Temporal Prediction of Unsteady Airfoil Aerodynamics Using Augmented Graph Neural Ordinary Differential Equations with Exogenous Controls](https://mlsanity.com/paper/2607.18309/) (2026)
- [Neural Field Ensembles for Aerodynamic Surface Prediction: Winning Solution to the ONERA CRM Wall Distribution 2025 Challenge](https://mlsanity.com/paper/2609.17160/) (2026)
- [Airfoil2Vec: Spectral Geometry-Conditioned Neural Surrogate Models for Airfoil Aerodynamics and a Downforce-Generating CFD Dataset](https://mlsanity.com/paper/2609.38213/) (2026)

## Abstract (arXiv)

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains for different flow conditions, handle non-parametric 3D geometric variations, and generalize to unseen shapes at test time. The coordinate-based formulation naturally leads to robustness with respect to discretization, allowing an excellent trade-off between computational cost (memory footprint and training time) and accuracy. The method is demonstrated on two industrially relevant applications: a RANS dataset of the two-dimensional compressible flow over a transonic airfoil and a dataset of the surface pressure distribution over 3D wings, including shape, inflow condition, and control surface deflection variations. On the considered test cases, our approach achieves a more than three times lower test error and significantly improves generalization error on unseen geometries compared to state-of-the-art Graph Neural Network architectures. Remarkably, the method can perform inference five order of magnitude faster than the high fidelity solver on the RANS transonic airfoil dataset. Code is available at https://gitlab.isae-supaero.fr/gi.catalani/aero-nepf