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Bayesian Optimization of a Lightweight and Accurate Neural Network for Aerodynamic Performance Prediction

James M. Shihua, Paul Saves, Rhea P. Liem, Joseph Morlier

TL;DR

The paper tackles the costly evaluations in aerospace MDO by combining Bayesian optimization with a lightweight neural network to predict aerodynamic performance. It uses SMT2.0 to handle mixed-type hyperparameters via specialized kernels and a KPLS feature space, optimizing a 5-hyperparameter NN (layers and activations) with Efficient Global Optimization, while training with Levenberg–Marquardt. The optimized NN achieves a cross-validation MAPE of $0.0163\%$ for drag prediction, an order of magnitude improvement over the baseline, and outperforms public NN models, including NeuralFoil, with far fewer parameters. An additional aircraft self-noise benchmark reports a MAPE of $0.82\%$, significantly beating the Kaggle winner, demonstrating the method’s robustness and potential to scale to large-scale MDO problems with reduced computational cost.

Abstract

Ensuring high accuracy and efficiency of predictive models is paramount in the aerospace industry, particularly in the context of multidisciplinary design and optimization processes. These processes often require numerous evaluations of complex objective functions, which can be computationally expensive and time-consuming. To build efficient and accurate predictive models, we propose a new approach that leverages Bayesian Optimization (BO) to optimize the hyper-parameters of a lightweight and accurate Neural Network (NN) for aerodynamic performance prediction. To clearly describe the interplay between design variables, hierarchical and categorical kernels are used in the BO formulation. We demonstrate the efficiency of our approach through two comprehensive case studies, where the optimized NN significantly outperforms baseline models and other publicly available NNs in terms of accuracy and parameter efficiency. For the drag coefficient prediction task, the Mean Absolute Percentage Error (MAPE) of our optimized model drops from 0.1433\% to 0.0163\%, which is nearly an order of magnitude improvement over the baseline model. Additionally, our model achieves a MAPE of 0.82\% on a benchmark aircraft self-noise prediction problem, significantly outperforming existing models (where their MAPE values are around 2 to 3\%) while requiring less computational resources. The results highlight the potential of our framework to enhance the scalability and performance of NNs in large-scale MDO problems, offering a promising solution for the aerospace industry.

Bayesian Optimization of a Lightweight and Accurate Neural Network for Aerodynamic Performance Prediction

TL;DR

The paper tackles the costly evaluations in aerospace MDO by combining Bayesian optimization with a lightweight neural network to predict aerodynamic performance. It uses SMT2.0 to handle mixed-type hyperparameters via specialized kernels and a KPLS feature space, optimizing a 5-hyperparameter NN (layers and activations) with Efficient Global Optimization, while training with Levenberg–Marquardt. The optimized NN achieves a cross-validation MAPE of for drag prediction, an order of magnitude improvement over the baseline, and outperforms public NN models, including NeuralFoil, with far fewer parameters. An additional aircraft self-noise benchmark reports a MAPE of , significantly beating the Kaggle winner, demonstrating the method’s robustness and potential to scale to large-scale MDO problems with reduced computational cost.

Abstract

Ensuring high accuracy and efficiency of predictive models is paramount in the aerospace industry, particularly in the context of multidisciplinary design and optimization processes. These processes often require numerous evaluations of complex objective functions, which can be computationally expensive and time-consuming. To build efficient and accurate predictive models, we propose a new approach that leverages Bayesian Optimization (BO) to optimize the hyper-parameters of a lightweight and accurate Neural Network (NN) for aerodynamic performance prediction. To clearly describe the interplay between design variables, hierarchical and categorical kernels are used in the BO formulation. We demonstrate the efficiency of our approach through two comprehensive case studies, where the optimized NN significantly outperforms baseline models and other publicly available NNs in terms of accuracy and parameter efficiency. For the drag coefficient prediction task, the Mean Absolute Percentage Error (MAPE) of our optimized model drops from 0.1433\% to 0.0163\%, which is nearly an order of magnitude improvement over the baseline model. Additionally, our model achieves a MAPE of 0.82\% on a benchmark aircraft self-noise prediction problem, significantly outperforming existing models (where their MAPE values are around 2 to 3\%) while requiring less computational resources. The results highlight the potential of our framework to enhance the scalability and performance of NNs in large-scale MDO problems, offering a promising solution for the aerospace industry.

Paper Structure

This paper contains 13 sections, 20 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Baseline Neural Network Design
  3. Bayesian Optimization
  4. Results
  5. Performance Metrics
  6. MSE
  7. RMSE
  8. MAPE
  9. PE
  10. Optimization of the Baseline NN
  11. Comparison with Other NN Models
  12. Additional Benchmark Problem: Aircraft Self Noise
  13. Conclusion

Figures (4)

  • Figure 1: BO optimizes the hyper-parameters of the NN which predicts the aerodynamic performance from shape parameterization and flow condition.
  • Figure 2: A sample plot showing an MLP architecture. The shown number of nodes is only for illustration (figure adapted from audet2022general).
  • Figure 3: Error distribution of the baseline and optimized model.
  • Figure 4: GP's prediction on MAPE given $N_1$ and $N_2$ with all other variables fixed, where solid red dots are collected samples during the BO process.