# Machine Learning in Aerodynamic Shape Optimization

arXiv: https://arxiv.org/abs/2202.07141 · HTML: https://mlsanity.com/paper/2202.07141/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 61 of its 525 references that are in the map.
- First posted on arXiv 15 Feb 2022.

## Builds on (most cited first, 30 of 61)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Deep Reinforcement Learning for Robotic Manipulation with Asynchronous Off-Policy Updates](https://mlsanity.com/paper/1610.00633/) (2016)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [A Survey on Deep Semi-supervised Learning](https://mlsanity.com/paper/2103.00550/) (2021)
- [An Introduction to Deep Reinforcement Learning](https://mlsanity.com/paper/1811.12560/) (2018)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [A guide to convolution arithmetic for deep learning](https://mlsanity.com/paper/1603.07285/) (2016)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Deep Learning for Anomaly Detection: A Review](https://mlsanity.com/paper/2007.02500/) (2020)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Independently Recurrent Neural Network (IndRNN): Building A Longer and Deeper RNN](https://mlsanity.com/paper/1803.04831/) (2018)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Pros and Cons of GAN Evaluation Measures: New Developments](https://mlsanity.com/paper/2103.09396/) (2021)
- [An Overview of Deep Semi-Supervised Learning](https://mlsanity.com/paper/2006.05278/) (2020)
- [Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition](https://mlsanity.com/paper/1402.1128/) (2014)
- [Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics](https://mlsanity.com/paper/2012.04728/) (2020)
- [Deep Learning vs. Traditional Computer Vision](https://mlsanity.com/paper/1910.13796/) (2019)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [A Survey of Deep Reinforcement Learning in Video Games](https://mlsanity.com/paper/1912.10944/) (2019)

## Built on by (most cited first, 30 of 39)

- [Improving aircraft performance using machine learning: a review](https://mlsanity.com/paper/2210.11481/) (2022)
- [Ship-D: Ship Hull Dataset for Design Optimization using Machine Learning](https://mlsanity.com/paper/2305.08279/) (2023)
- [Multi-fidelity Bayesian Optimization: A Review](https://mlsanity.com/paper/2311.13050/) (2023)
- [On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it](https://mlsanity.com/paper/2302.07557/) (2023)
- [Parametric Generative Schemes with Geometric Constraints for Encoding and Synthesizing Airfoils](https://mlsanity.com/paper/2205.02458/) (2022)
- [Towards aerodynamic surrogate modeling based on β-variational autoencoders](https://mlsanity.com/paper/2408.04969/) (2024)
- [Overtone: Cyclic Patch Modulation for Clean, Efficient, and Flexible Physics Emulators](https://mlsanity.com/paper/2507.09264/) (2025)
- [Implicitly Guided Design with PropEn: Match your Data to Follow the Gradient](https://mlsanity.com/paper/2405.18075/) (2024)
- [ONERA's CRM WBPN database for machine learning activities, related regression challenge and first results](https://mlsanity.com/paper/2505.06265/) (2025)
- [A Manifold-based Airfoil Geometric-feature Extraction and Discrepant Data Fusion Learning Method](https://mlsanity.com/paper/2206.12254/) (2022)
- [Enhancing Vehicle Aerodynamics with Deep Reinforcement Learning in Voxelised Models](https://mlsanity.com/paper/2405.11492/) (2024)
- [A Survey on Design-space Dimensionality Reduction Methods for Shape Optimization](https://mlsanity.com/paper/2405.13944/) (2024)
- [Generative Aerodynamic Design with Diffusion Probabilistic Models](https://mlsanity.com/paper/2409.13328/) (2024)
- [MaNGO - Adaptable Graph Network Simulators via Meta-Learning](https://mlsanity.com/paper/2510.05874/) (2025)
- [3DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization](https://mlsanity.com/paper/2512.08987/) (2025)
- [Tailoring Generative Adversarial Networks for Smooth Airfoil Design](https://mlsanity.com/paper/2404.11816/) (2024)
- [Rapid aerodynamic prediction of swept wings via physics-embedded transfer learning](https://mlsanity.com/paper/2409.12711/) (2024)
- [Three-dimensional Deep Shape Optimization with a Limited Dataset](https://mlsanity.com/paper/2506.12326/) (2025)
- [Knowledge-embedded meta-learning model for lift coefficient prediction of airfoils](https://mlsanity.com/paper/2303.02844/) (2023)
- [Accelerated Airfoil Design Using Neural Network Approaches](https://mlsanity.com/paper/2503.24052/) (2025)
- [Context-aware Learned Mesh-based Simulation via Trajectory-Level Meta-Learning](https://mlsanity.com/paper/2511.05234/) (2025)
- [Uncertainty-Aware Data-Based Method for Fast and Reliable Shape Optimization](https://mlsanity.com/paper/2601.21956/) (2026)
- [Latent Task-Specific Graph Network Simulators](https://mlsanity.com/paper/2311.05256/) (2023)
- [The Principle of Minimum Pressure Gradient: An Alternative Basis for Physics-Informed Learning of Incompressible Fluid Mechanics](https://mlsanity.com/paper/2401.07489/) (2024)
- [A Multi-Fidelity Methodology for Reduced Order Models with High-Dimensional Inputs](https://mlsanity.com/paper/2402.17061/) (2024)
- [A mechanism-driven reinforcement learning framework for shape optimization of airfoils](https://mlsanity.com/paper/2403.04329/) (2024)
- [Jacobian-Enhanced Neural Networks](https://mlsanity.com/paper/2406.09132/) (2024)
- [FuncGenFoil: Airfoil Generation and Editing Model in Function Space](https://mlsanity.com/paper/2502.10712/) (2025)
- [AutoTandemML: Active Learning Enhanced Tandem Neural Networks for Inverse Design Problems](https://mlsanity.com/paper/2502.15643/) (2025)
- [LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs](https://mlsanity.com/paper/2506.17582/) (2025)

## Abstract (arXiv)

Machine learning (ML) has been increasingly used to aid aerodynamic shape optimization (ASO), thanks to the availability of aerodynamic data and continued developments in deep learning. We review the applications of ML in ASO to date and provide a perspective on the state-of-the-art and future directions. We first introduce conventional ASO and current challenges. Next, we introduce ML fundamentals and detail ML algorithms that have been successful in ASO. Then, we review ML applications to ASO addressing three aspects: compact geometric design space, fast aerodynamic analysis, and efficient optimization architecture. In addition to providing a comprehensive summary of the research, we comment on the practicality and effectiveness of the developed methods. We show how cutting-edge ML approaches can benefit ASO and address challenging demands, such as interactive design optimization. Practical large-scale design optimizations remain a challenge because of the high cost of ML training. Further research on coupling ML model construction with prior experience and knowledge, such as physics-informed ML, is recommended to solve large-scale ASO problems.