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Machine Learning in Aerodynamic Shape Optimization

Jichao Li, Xiaosong Du, Joaquim R. R. A. Martins

arXiv:2202.07141v2cs.LGmath.OCphysics.flu-dyn

TL;DR

ASO requires efficient optimization despite costly aerodynamic analyses, high-dimensional designs, and demanding multiobjective and interactive settings. This review synthesizes ML methods for compact geometric representation, aerodynamic prediction, and optimization architecture. It finds that ML broadens ASO capabilities, while large-scale applications remain limited by training cost and motivate physics-informed and experience-informed approaches.

  • Problem

    High-dimensional ASO involves costly aerodynamic analyses, while multiobjective and interactive optimization remain computationally demanding.

  • Method

    The review surveys ML algorithms and applications addressing geometric design spaces, aerodynamic evaluation, and optimization architectures in ASO.

  • Results

    ML has improved ASO scope and effectiveness and supports compact parameterization, aerodynamic prediction, surrogate optimization, interactive design, and derivative-free optimization.

  • Takeaways & Limitations

    ML can address ASO challenges including discontinuous functions, multiple objectives, uncertainties, and interactive design, while physics-informed models may improve extrapolation and data efficiency.

  • Takeaways & Limitations

    Large-scale ASO remains challenging because ML training requires extensive design-space coverage, and RL has difficulty with training efficiency and adjustable constraints.

Abstract

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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.

Acronyms

The paper defines abbreviations for aerodynamic optimization, machine learning, modeling, and computational methods used throughout the review.

  • ASO denotes aerodynamic shape optimization, while ML denotes machine learning and CFD denotes computational fluid dynamics.
  • The abbreviation list includes learning architectures such as ANN, CNN, DBN, DNN, GAN, LSTM, RNN, SVM, and VAE.
  • Optimization and uncertainty methods include EGO, MCMC, RL, DRL, PCA, POD, SVD, and PINN.
  • Geometric and aerodynamic modeling terms include FFD, CRM, DMD, GEK, GMM, GTM, KNN, ME, and PCE.

Symbols

The paper uses standard aerodynamic symbols for flow conditions and performance coefficients.

  • α denotes angle of attack, M denotes Mach number, and Re denotes Reynolds number.
  • CD, CL, and CM denote drag, lift, and moment coefficients, respectively.

1. Introduction

The introduction positions ML as a data-driven complement to conventional ASO, motivated by expensive high-dimensional optimization and enabled by aerodynamic data and improved learning methods. The review synthesizes ML applications across design parameterization, aerodynamic evaluation, and optimization architecture.

  • CFD-based ASO advances aircraft-component design and can reduce development cycle time while improving design performance.
  • Gradient-based ASO efficiently searches high-dimensional spaces because adjoint derivatives have computational cost independent of the number of design variables.
  • ML models can predict physical behavior without repeatedly solving governing equations, provided that sufficient training data support accurate and general predictions.
  • Aerodynamic data come from historical designs, current practical designs, and newly generated CFD simulations, supporting surrogate models and physics-informed neural networks.
  • ML application is difficult for large-scale high-dimensional ASO because training samples must adequately cover all design-variable dimensions.
  • The review summarizes ML approaches and ASO applications, assesses their effectiveness and practicality, and discusses future prospects.

2. Aerodynamic Shape Optimization

Conventional CFD-based ASO combines geometric parameterization, aerodynamic analysis, derivative computation, and iterative optimization, but faces challenges from high-dimensional shapes, expensive evaluations, uncertainty, heterogeneous models, and slow interaction. ML is presented as a means to make these stages more compact, faster, and more efficient.

  • Scope: This review focuses on fixed-configuration aerodynamic design, particularly local sectional shape design, rather than multidisciplinary configuration changes.
  • General Process: ASO defines objectives, constraints, and design variables, with aerodynamic performance evaluated across flight conditions such as Mach and Reynolds numbers.
  • Geometric Parameterization: NACA and PARSEC provide reasonable shapes with limited variables, whereas CST and FFD offer greater geometric freedom by increasing variable count.
  • Existing Challenges: High aerodynamic-analysis cost and high-dimensional geometric spaces are compounding ASO challenges, making efficient gradient-based optimization important.
  • General Process: The MACH-Aero workflow iteratively deforms the mesh, evaluates the new shape, computes adjoint derivatives, and updates design variables through the optimizer.
  • General Process: MACH-Aero modularly combines parameterization, mesh deformation, CFD evaluation, adjoint solvers, and gradient-based optimizers through Python interfaces.
  • Existing Challenges: Conventional parameterizations can create abnormal shapes and require many variables, unnecessarily complicating optimization and increasing computational demands.
  • Existing Challenges: Multiobjective CFD optimization is expensive in high-dimensional spaces, and sequential single-objective solutions may yield only a few nonuniform Pareto-front points.

3. Machine Learning Methods

Machine learning algorithms learn patterns from data and can simplify problems whose solutions would otherwise require extensive rule-based programming. They are categorized by how they compare data, use supervision, and update from experience.

  • ML algorithms learn from experience for a task and performance measure, improving performance as experience accumulates.
  • ML approaches are classified by whether they compare new data with training data or construct predictive models.
  • ML algorithms differ according to whether training uses human supervision and whether learning occurs in batches or incrementally.
  • Most ML methods construct models for prediction, while instance-based methods such as KNN compare new samples with training data.
  • The section provides a self-contained overview of ML approaches used successfully in aerodynamic shape optimization.

3.1. Supervised Learning

Supervised learning maps inputs to observed targets through classification or regression, while ASO applications use methods including KNN, SVM, random forests, and kriging. These methods support prediction and surrogate modeling, but their effectiveness depends on choices such as neighborhood size, training data, and model assumptions.

  • 3.1. Supervised Learning: Supervised learning trains on inputs paired with labels or targets; classification predicts discrete categories, whereas regression predicts continuous observations.
  • 3.1.1. k-Nearest Neighbors: KNN predicts by selecting the k nearest training samples using a distance measure, then applying majority voting for classification or neighbor means for regression.Distance choices include Euclidean, Manhattan, Minkowski, and Hamming measures; distance-weighted predictions can give closer neighbors greater influence.
  • 3.1.1. k-Nearest Neighbors: KNN is simple and flexible, but choosing k is difficult: small values can be noisy, while large values may oversmooth and misrepresent the output space.The heuristic k = √n is suggested, but it is not guaranteed to be optimal.
  • 3.1.1. k-Nearest Neighbors: 3.3% average relative error was achieved when KNN estimated wind speed from rotary-wing drone flight data after studying the optimal k value.
  • 3.1.2. Support Vector Machines: SVM uses kernels and regularization to construct hyperplanes for classification or regression, with support vectors determining the prediction.For classification, the optimal hyperplane maximizes the margin; for regression, deviations outside an ϵ-tube are penalized.
  • 3.1.2. Support Vector Machines: An SVM surrogate estimated lift-to-drag ratio in ASO with 14 input parameters for a two-dimensional case and 36 inputs for a three-dimensional case.
  • 3.1.3. Decision Tree and Random Forest: Decision trees select splits using information gain or Gini gain, while random forests combine multiple trees and aggregate their classifications or regression predictions.Random forests address the overfitting risk of a single deep tree through bootstrapping and feature randomness.

3.2. Unsupervised Learning

Unsupervised learning analyzes unlabeled data to discover patterns, including clusters and lower-dimensional representations. In ASO, clustering and dimensionality reduction support surrogate modeling and reduced-order aerodynamic prediction, with method choice depending on data geometry and task.

  • Overview: Unsupervised learning discovers patterns in unlabeled data and includes clustering and dimensionality reduction.Dimensionality reduction transforms high-dimensional data into lower-dimensional representations while retaining key properties.
  • k-means: k-means assigns samples to user-defined clusters through expectation-maximization updates of cluster memberships and arithmetic-mean centers.Convergence occurs when cluster centers no longer change.
  • PCE and kriging: Around 50 samples reduced RMSE to 1% of testing-label standard deviation for PC-Cokriging, compared with around 100 for PC-Kriging and LARS-based PCE.Cokriging required more than 100 samples because the low-fidelity model was not highly correlated with the Currin function.
  • k-means: k-means is fast and robust for well-separated data but may miss global optima, requires a preset cluster count, and produces only linear boundaries.These limitations make it less suitable for complex-geometry clustering problems.
  • ASO applications: k-means clustering selected radial-basis-function centers for aerodynamic force and moment surrogate modeling, achieving success on real-time aircraft flight data.The application used an RBF neural network for aerodynamic parameter estimation.
  • GMM: GMM models clusters with Gaussian means and covariance structures, and its aerodynamic use supported mixture-of-experts GEK surrogates for conventional and unconventional aircraft.Unlike k-means, GMM considers covariance structure and avoids imposing certain mean or cluster-size biases.
  • Dimensionality reduction: Nonlinear dimensionality reduction performed better near shocks and discontinuities, whereas linear methods outperformed nonlinear methods for steady-state prediction.Nonlinear representations also reduced evaluation costs for nonlinear reduced-order models and often improved shock-region accuracy.

3.3. Semi-Supervised Learning

Semi-supervised learning combines limited labeled data with abundant unlabeled data, addressing settings where labels such as experimental aerodynamic measurements are costly or incomplete. In ASO, DBNs use stacked RBMs for unsupervised representation learning followed by supervised fine-tuning, although training remains challenging.

  • Overview: Semi-supervised learning combines a small labeled set with a large unlabeled set when aerodynamic labels are incomplete or costly.The approach trains models by combining existing labels with pseudo-labels for unlabeled data.
  • Overview: Semi-supervised learning iteratively predicts pseudo-labels for unlabeled data and retrains a model until predictive performance no longer changes.The resulting model is used for regression on query data.
  • Deep belief networks: A DBN is a stack of RBMs that learns input distributions through unsupervised pretraining and can be fine-tuned with supervised gradient descent and backpropagation.RBMs connect visible and hidden layers but not nodes within the same layer, enabling efficient training.
  • RBM training: Contrastive divergence trains RBMs by contrasting gradients from observed data with gradients from Gibbs-reconstructed samples, then updating weights and biases.The forward pass produces the positive gradient, while reconstructed visible and hidden states produce the negative gradient.
  • RBM training: RBM hidden activations can serve as features for other models, but RBM training remains challenging even with contrastive divergence.RBMs are computationally more efficient than traditional Boltzmann machines because intra-layer connections are restricted.

3.4. Reinforcement Learning

Reinforcement learning addresses sequential decision problems by learning policies through interaction with an environment and feedback rewards. Deep RL uses neural networks to handle complex, high-dimensional states, with value-based methods suited to discrete actions and policy-based methods suited to continuous or high-dimensional action spaces.

  • RL foundations: RL learns an agent policy by repeatedly observing states, taking actions, receiving rewards, and updating decisions.Training seeks a policy that maximizes total accumulated reward.
  • RL foundations: A state describes the environment, an action is a possible move, and a reward measures action quality, potentially immediately or after delay.The discount factor weights future rewards in value estimates.
  • RL foundations: Model-based RL predicts action outcomes with transition and reward models, whereas model-free RL learns directly through environment interaction.Both approaches seek an optimal policy and can be described using transition probabilities and reward functions.
  • Deep RL: Deep RL uses neural networks to model policies or value functions, enabling RL to address large-scale complex problems and high-dimensional states.Unlike supervised learning, DRL receives rewards from the environment rather than predefined ground-truth labels.
  • Value-based methods: Deep Q-networks approximate Q-values with a DNN and select actions using value estimates, typically with epsilon-greedy exploration.They are generally applicable to discrete action spaces.
  • Policy-based methods: Policy-based DRL directly models action policies, making it applicable to continuous action spaces, while policy-based methods may become stuck at local optima.The policy is updated to increase probabilities of high-return actions and decrease probabilities of low-return actions.

3.5. Artificial Neural Networks

Artificial neural networks are central to deep learning and recent ML-based ASO, mapping input parameters to predicted quantities through layered nonlinear transformations. Their training relies mainly on gradient-based optimization, while architectures such as CNNs exploit structured inputs with fewer parameters and hierarchical feature extraction.

  • ANN fundamentals: ANNs are scalable deep-learning models widely used in recent ML-based ASO for large-scale and complex tasks.A deep stack of hidden layers forms a deep neural network.
  • ANN fundamentals: Each neuron maps inputs to an output through weighted summation, bias addition, and an activation function that introduces nonlinearity.The activation function’s monotonicity, range, and differentiability guide its selection.
  • Model training: ANN training minimizes squared prediction error by iteratively adjusting weights and biases with gradient-based optimization.Gradient descent uses a learning rate that is commonly reduced toward the end of training.
  • Model training: Batch, stochastic, and mini-batch gradient descent trade off full-data accuracy, training speed, and movement away from local minima.Mini-batch gradient descent lies between batch and stochastic gradient descent in data usage and behavior.
  • Convolutional neural networks: CNNs process structured inputs with convolutional, pooling, and fully connected layers while reducing parameter counts through filters.Convolutional layers extract local and global information, and pooling reduces dimensionality to help avoid overfitting.
  • Convolutional neural networks: CNNs learn spatial hierarchies and reuse weights across locations, improving recognition efficiency for large-scale structured inputs.Their translation-invariant behavior allows learned patterns to be identified at different positions.

3.5.4. Recurrent Neural Networks

Recurrent architectures process sequential inputs using hidden states, while LSTM adds gates that improve long-term dependency modeling. Autoencoders, VAEs, and GANs extend neural representation learning and generation for aerodynamic design applications, with practical trade-offs in complexity and training stability.

  • Recurrent Neural Networks: RNNs pass each time-step input and the previous hidden state through recurrent structures to predict outputs and continue the sequence.This recurrent feedback gives RNNs memory of historical information and makes them suitable for time-sequence data.
  • Recurrent Neural Networks: RNNs suffer from long-term dependencies because, in practice, they may fail to connect relevant information far apart in memory.LSTM addresses this limitation by adding forget, update, and output gates.
  • Recurrent Neural Networks: LSTM updates cell and hidden states through gated transformations of current inputs and previous states, retaining or discarding information across time steps.The forget gate scales the previous cell state, the update gate contributes a candidate cell state, and the output gate controls the hidden state.
  • Recurrent Neural Networks: LSTM models long-term dependencies more robustly than vanilla RNNs, but its added gates increase computing complexity and memory requirements.In aerospace engineering, LSTM has mainly been used to predict unsteady aerodynamic quantities.
  • Representation Learning: Autoencoders compress unlabeled high-dimensional data through an encoder, bottleneck layer, and decoder, while VAEs infer latent distributions for generating related data.In ASO, autoencoder representations enabled more local geometry modifications and improved optimization performance, while VAE variables represented supercritical-airfoil flow fields.
  • Generative Models: GANs train a generator and discriminator adversarially to produce data resembling the training set, and curve-fitting GANs have been applied to smooth airfoil and wing-section parameterization.These models shortened optimization iterations with almost no penalty on optimal performance in reported ASO applications.
  • Generative Models: GAN training can be difficult because equilibrium is hard to reach and mode collapse can restrict outputs to a small set of repeated samples.Wasserstein loss is described as a mitigation, but weight clipping can cause unstable training or slow convergence.

3.5.7. Self-organizing Maps

Self-organizing maps provide topology-preserving low-dimensional representations for interpreting and visualizing high-dimensional data. Their advantages include interpretability, but categorical or mixed data and slow training remain limitations.

  • Self-organizing Maps: A self-organizing map uses unsupervised learning to project high-dimensional observations onto low-dimensional nodes while preserving neighborhood topology.Neighboring observations in the input space are mapped to neighboring nodes, supporting visualization of hidden structures such as clusters.
  • Self-organizing Maps: SOMs make data easier to interpret and can address several classification problems while providing a compact summary of the data.Their preparation time is slow, making SOMs difficult to train.
  • Self-organizing Maps: SOMs perform poorly on categorical data and even worse on mixed data types.This limitation constrains their suitability when the input representation combines heterogeneous variable types.
  • Physics-Informed Neural Networks: Physics-informed neural networks incorporate governing physical laws into machine-learning training through partial-differential-equation residual penalties.The original PINN formulation assumes fixed initial and boundary conditions, creating challenges when ASO boundary conditions vary after each iteration.
  • Self-organizing Maps: SOMs are trained through competitive learning by selecting a sample, identifying the best matching unit, and updating that unit and nearby nodes.The best matching unit is the node whose weights have the shortest Euclidean distance from the selected training sample.

4. Machine Learning in Aerodynamic Shape Optimization

ML can improve ASO through compact geometric parameterizations, low-cost aerodynamic prediction, and more efficient optimization workflows. The review organizes applications around these three aspects and evaluates their practicality and effectiveness.

  • Review Scope: ASO efficiency is mainly governed by geometric design-space dimensionality, aerodynamic-analysis cost, and optimization convergence rate.The review examines ML methods that address each of these three factors.

4.1. Geometric Design Space

ML-based modal parameterization and geometric filtering make aerodynamic design spaces more compact, interpretable, and suitable for optimization. Research has progressed from linear modes and engineering rules toward nonlinear generative models and learned validity constraints for airfoils and wings.

  • Motivation: Conventional geometric parameterizations use many variables, creating abnormal shapes that can hinder CFD convergence and optimization.Reducing dimensionality and excluding abnormal candidates are therefore central geometric-design-space goals.
  • Modal Parameterization: Modal parameterization controls aerodynamic shapes with global modes derived from samples, unlike CST, Hicks–Henne, and FFD local deformations.Modes may be linear or nonlinear, and they couple design variables to improve geometric efficiency.
  • Modal Parameterization: PCA and active subspace methods provide linear low-dimensional representations, with active subspaces targeting directions that most influence objectives such as lift and drag.ASM modes have been applied to aircraft-wing optimization and vehicle aerodynamic analysis.
  • Modal Parameterization: Deep-learning models including GANs, VAEs, GTM, and nonlinear manifolds extend modal parameterization toward realistic nonlinear airfoil, wing, and other aerodynamic shapes.GAN-based approaches can generate smooth or realistic shapes, while applications have expanded from two-dimensional airfoils to three-dimensional wings.
  • Modal Parameterization: Pre-optimization-derived modes produced another 0.25% gain in adiabatic efficiency within an 8-D NASA Rotor 37 blade design space.However, pre-optimization is time-consuming and may produce insufficient shape diversity when good designs are far from the optimum.
  • Geometric Filtering: Geometric filtering uses learned validity models to exclude abnormal shapes while preserving innovative designs and improving surrogate-model training data.In 216 airfoil optimizations and several wing optimizations, a validity lower bound of ∼0.7 did not exclude cruise-efficiency-maximizing shapes in the investigated transonic regime.

4.2. Aerodynamic Evaluation

ML-based aerodynamic evaluation uses surrogates, dimensionality reduction, and physics-informed models to accelerate coefficient, flow-field, and constraint prediction. These methods can support interactive optimization, but training cost, extrapolation, nonlinear flow behavior, and preservation of integral quantities remain important limitations.

  • Aerodynamic coefficient modeling: Sparse polynomial-chaos surrogates reduce training cost through linear regression, lower-order truncation, and early stopping, while PC-Kriging combines predictive confidence with analytical statistics.Gradient-enhanced PC-Kriging improved performance and robustness across airfoil, blended-wing-body, and wing aerostructural design cases.
  • Aerodynamic coefficient modeling: Neural-network surrogates can handle large aerodynamic datasets and support interactive design optimization with accurate coefficient predictions.Reported applications used about 100,000 training samples and achieved low errors for lift and drag; another study found errors within 0.4% on 47,967 unseen wing samples.
  • Aerodynamic coefficient modeling: 400 seconds of training reduced airfoil prediction root mean square error by 2% ∼45% for Cl and 2% ∼19% for Cd versus a traditional Gaussian process.The deep Gaussian process required substantially more training time than the traditional Gaussian process, which took 0.1 ∼1 second.
  • Flow field modeling: Flow-field modeling commonly reduces high-dimensional CFD fields with POD, but its low-dimensional linear-subspace assumption makes nonlinear phenomena such as shock waves difficult to represent.Adaptive sampling, multiple local subspaces, and shifted bases improve prediction in strongly nonlinear or transonic regimes, but may require substantial physics understanding.
  • Physics-informed evaluation: Physics-informed models can encode governing equations such as RANS and potentially improve accuracy, generalization, and extrapolation, but benchmark ASO evidence remains limited.The review recommends clearer demonstrations of extrapolation and deeper comparisons with conventional approaches such as POD with kriging.
  • Flow field modeling: Low-dimensional flow-field models may fail to preserve global integral quantities, so directly modeling aerodynamic functions can outperform modeling fields before evaluating those functions.For intake-port design, POD-plus-kriging velocity-field modeling was worse than directly modeling mass flow and tumble.

4.3. Optimization Architecture

ML enables new ASO architectures that reduce reliance on costly CFD evaluations, support interactive design, and accelerate surrogate-based and inverse-design workflows. However, training cost, adjustable constraints, and generalization remain important limitations.

  • Reinforcement-learning-based Optimization: RL policies can achieve gradient-based optimization speed without aerodynamic derivatives, but training may be time-consuming and adjustable constraints are difficult to handle.Conditional generative models offer fast inverse design, yet generated shapes may miss target conditions and remain distinct from optimal airfoils.
  • Surrogate-based Optimization: Surrogate-based optimization combines initial design-of-experiment sampling with iterative infill refinement, with performance governed by surrogate efficiency, design-space size, and infilling effectiveness.ML improves this architecture through more accurate surrogate models, compact parameterizations, and more efficient infill criteria.
  • Surrogate-based Optimization: 40 learned wing modes matched 192-variable CFD-based optimization within 0.3 drag count after 600–800 CFD evaluations including training cost.The 192-variable surrogate optimization failed to improve the baseline after 1000 CFD simulations, whereas PCA modes extracted from deep-learning-based samples substantially improved convergence efficiency.
  • Interactive Design Optimization: Webfoil provides fast interactive airfoil analysis and optimization using surrogate models trained from more than 100,000 RANS airfoil analyses.Mean relative errors for predicted Cl, Cd, and Cm were 0.145%, 0.255%, and 0.160% in subsonic cases, with larger errors in transonic cases.
  • Interactive Design Optimization: Wing aerodynamic models trained on 135,108 RANS samples achieved mean relative errors within 0.4% on 47,967 unseen shapes and produced optimized wings within one to two drag counts of CFD results.The models supported single-point, multipoint, and multiobjective optimization of high-dimensional wing shapes.
  • Interactive Design Optimization: Gradient-free optimization can be impractical for interactive ASO: PSO required half a million evaluations for a solution comparable to SLSQP, while NSGA-II failed to match SLSQP after one million evaluations.These costs remain problematic even when data-based aerodynamic analyses are cheap, particularly when geometric constraints require mesh deformation.

5. Conclusions and Outlook

The review finds that ML can improve geometric parameterization, aerodynamic prediction, and optimization architectures in ASO. Its practical use remains bounded by data and training costs, extrapolation, limited comparisons with conventional methods, and incomplete treatment of multidisciplinary effects.

  • Conclusions: ML reduces geometric design-space dimensionality or restricts bounds by learning from designer knowledge, historical designs, or low-fidelity optimization results.Well-trained parameterizations can exclude abnormal shapes while retaining a low probability of excluding innovative shapes.
  • Conclusions: ML improves aerodynamic-coefficient prediction and supports nonlinear dimensionality reduction, accelerated high-fidelity simulation, inverse design, and design optimization.Most prediction models remain interpolative, while PINNs are identified as a potential route beyond interpolation.
  • Conclusions: ML contributes surrogate-based, interactive, reinforcement-learning, and conditional-generative optimization architectures for ASO.Interactive design has been demonstrated for airfoils, wings, and aircraft; RL demonstrations remain limited to problems with few design variables.
  • Conclusions: Many ML studies address less challenging ASO problems without comparison to conventional ASO, so future work should target intractable problems and compare against state-of-the-art methods.The review identifies solving problems that conventional methods cannot handle as ML's core strength rather than replacing effective conventional optimization.
  • Outlook: Large-scale ASO remains constrained by high-fidelity data costs, with interactive airfoil and wing design datasets reaching 10^5 samples.The review recommends more data-efficient sampling and extrapolatory prediction models, including further validation of PINNs.
  • Outlook: ML studies often lack coupled simulation and experimental data, limiting industrial practicality and motivating stronger industry–academia collaboration.Experimental data are less accessible to academic researchers because they depend on specialized facilities.
  • Outlook: ML is not a replacement for adjoint-based CFD optimization, which remains suitable for deterministic, non-multimodal, large-scale high-dimensional ASO problems.The review recommends maintaining familiarity with conventional methods alongside continued ML development.
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