# Enhanced data efficiency using deep neural networks and Gaussian processes for aerodynamic design optimization

arXiv: https://arxiv.org/abs/2008.06731 · HTML: https://mlsanity.com/paper/2008.06731/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2020.

## Built on by (most cited first, 15 of 15)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils](https://mlsanity.com/paper/2302.00807/) (2023)
- [Inverse design optimization framework via a two-step deep learning approach: application to a wind turbine airfoil](https://mlsanity.com/paper/2108.08500/) (2021)
- [Fusion-DeepONet: A Data-Efficient Neural Operator for Geometry-Dependent Hypersonic and Supersonic Flows](https://mlsanity.com/paper/2501.01934/) (2025)
- [Multi-fidelity Bayesian Optimization: A Review](https://mlsanity.com/paper/2311.13050/) (2023)
- [Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles](https://mlsanity.com/paper/2302.09748/) (2023)
- [SuperWing: a comprehensive transonic wing dataset for data-driven aerodynamic design](https://mlsanity.com/paper/2512.14397/) (2025)
- [Data-Driven Wind Turbine Wake Modeling via Probabilistic Machine Learning](https://mlsanity.com/paper/2109.02411/) (2021)
- [Real-time elastic partial shape matching using a neural network-based adjoint method](https://mlsanity.com/paper/2303.09343/) (2023)
- [Uncertainty-Aware Data-Based Method for Fast and Reliable Shape Optimization](https://mlsanity.com/paper/2601.21956/) (2026)
- [Multifidelity Cross-validation](https://mlsanity.com/paper/2407.01495/) (2024)
- [Machine-learning-based multipoint optimization of fluidic injection parameters for improving nozzle performance](https://mlsanity.com/paper/2409.12707/) (2024)
- [Scalable Gaussian process modeling of parametrized spatio-temporal fields](https://mlsanity.com/paper/2603.00290/) (2026)
- [Towards a Foundation-Model Paradigm for Aerodynamic Prediction in Three-dimensional Design](https://mlsanity.com/paper/2604.18062/) (2026)
- [A Bayesian latent Gaussian process framework for aerodynamic uncertainty quantification](https://mlsanity.com/paper/2606.28871/) (2026)

## Abstract (arXiv)

Adjoint-based optimization methods are attractive for aerodynamic shape design primarily due to their computational costs being independent of the dimensionality of the input space and their ability to generate high-fidelity gradients that can then be used in a gradient-based optimizer. This makes them very well suited for high-fidelity simulation based aerodynamic shape optimization of highly parametrized geometries such as aircraft wings. However, the development of adjoint-based solvers involve careful mathematical treatment and their implementation require detailed software development. Furthermore, they can become prohibitively expensive when multiple optimization problems are being solved, each requiring multiple restarts to circumvent local optima. In this work, we propose a machine learning enabled, surrogate-based framework that replaces the expensive adjoint solver, without compromising on predicting predictive accuracy. Specifically, we first train a deep neural network (DNN) from training data generated from evaluating the high-fidelity simulation model on a model-agnostic, design of experiments on the geometry shape parameters. The optimum shape may then be computed by using a gradient-based optimizer coupled with the trained DNN. Subsequently, we also perform a gradient-free Bayesian optimization, where the trained DNN is used as the prior mean. We observe that the latter framework (DNN-BO) improves upon the DNN-only based optimization strategy for the same computational cost. Overall, this framework predicts the true optimum with very high accuracy, while requiring far fewer high-fidelity function calls compared to the adjoint-based method. Furthermore, we show that multiple optimization problems can be solved with the same machine learning model with high accuracy, to amortize the offline costs associated with constructing our models.