# NeuralFoil: An Airfoil Aerodynamics Analysis Tool Using Physics-Informed Machine Learning

arXiv: https://arxiv.org/abs/2503.16323 · HTML: https://mlsanity.com/paper/2503.16323/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 52 references that are in the map.
- First posted on arXiv 20 Mar 2025.

## Builds on (most cited first, 5 of 5)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)
- [PySensors: A Python Package for Sparse Sensor Placement](https://mlsanity.com/paper/2102.13476/) (2021)

## Built on by (most cited first, 11 of 11)

- [Toward Autonomous Engineering Design: A Knowledge-Guided Multi-Agent Framework](https://mlsanity.com/paper/2511.03179/) (2025)
- [Transfer learning-enhanced deep reinforcement learning for aerodynamic airfoil optimisation subject to structural constraints](https://mlsanity.com/paper/2505.02634/) (2025)
- [Bayesian Optimization of a Lightweight and Accurate Neural Network for Aerodynamic Performance Prediction](https://mlsanity.com/paper/2503.19479/) (2025)
- [A Kernel-based Resource-efficient Neural Surrogate for Multi-fidelity Prediction of Aerodynamic Field](https://mlsanity.com/paper/2512.10287/) (2025)
- [In-Context Black-Box Optimization with Unreliable Feedback](https://mlsanity.com/paper/2605.06187/) (2026)
- [GLOBE: Accurate and Generalizable PDE Surrogates using Domain-Inspired Architectures and Equivariances](https://mlsanity.com/paper/2511.15856/) (2025)
- [Neural-Surrogate Co-Design of Aerodynamic Shape and Control](https://mlsanity.com/paper/2603.06760/) (2026)
- [Agentic Risk-Aware Set-Based Engineering Design](https://mlsanity.com/paper/2604.16687/) (2026)
- [AirfoilGen: A valid-by-construction and performance-aware latent diffusion model for airfoil generation](https://mlsanity.com/paper/2605.20303/) (2026)
- [CoFINN: Conservation Flux Informed Neural Networks for Physics Problems Governed by Conservation Laws](https://mlsanity.com/paper/2607.06587/) (2026)
- [Example-driven Parametrisations for Bayesian Shape Optimisation](https://mlsanity.com/paper/2610.11984/) (2026)

## Abstract (arXiv)

NeuralFoil is an open-source Python-based tool for rapid aerodynamics analysis of airfoils, similar in purpose to XFoil. Speedups ranging from 8x to 1,000x over XFoil are demonstrated, after controlling for equivalent accuracy. NeuralFoil computes both global and local quantities (lift, drag, velocity distribution, etc.) over a broad input space, including: an 18-dimensional space of airfoil shapes, possibly including control deflections; a 360 degree range of angles of attack; Reynolds numbers from 102 to 1010; subsonic flows up to the transonic drag rise; and with varying turbulence parameters. Results match those of XFoil closely: the mean relative error of drag is 0.37% on simple cases, and remains as low as 2.0% on a test dataset with numerous post-stall and transitional cases. NeuralFoil facilitates gradient-based design optimization, due to its C^∞-continuous solutions, automatic-differentiation-compatibility, and bounded computational cost without non-convergence issues. NeuralFoil is a hybrid of physics-informed machine learning techniques and analytical models. Here, physics information includes symmetries that are structurally embedded into the model architecture, feature engineering using domain knowledge, and guaranteed extrapolation to known limit cases. This work also introduces a new approach for surrogate model uncertainty quantification that enables robust design optimization. This work discusses the methodology and performance of NeuralFoil with several case studies, including a practical airfoil design optimization study including both aerodynamic and non-aerodynamic constraints. Here, NeuralFoil optimization is able to produce airfoils nearly identical in performance and shape to expert-designed airfoils within seconds; these computationally-optimized airfoils provide a useful starting point for further expert refinement.