Manifold-driven deep networks for aerodynamic pressure reconstruction and shape optimization

In aerodynamic shape optimization, dimensionality reduction is a key approach to alleviating the high computational cost and long runtimes associated with iterative computational fluid dynamics analyses. However, as modern engineering systems grow increasingly complex—often involving data on the order of millions to billions—traditional dimensionality reduction methods struggle to capture the nonlinear manifold structure inherent in high-dimensional data and suffer from limited generalization capabilities. In this work, we introduce a manifold-driven deep network optimization framework that enhances both efficiency and accuracy in aerodynamic design optimization. First, a Bayesian Gaussian process latent variable model (BGPLVM) performs nonlinear reduction on high-fidelity flow-field data, such as pressure distributions, thereby identifying a compact, low-dimensional latent space that preserves the essential aerodynamic features. Next, a deep neural network is trained as a multi-output surrogate model to map design variables to both global aerodynamic coefficients and coordinates in the latent space. Finally, a hybrid optimization strategy that combines global and gradient-based algorithms is applied to locate the optimal shape. Results from the GA(W)-1 airfoil and M6 wing cases show that the BGPLVM achieves nonlinear reduction of high-dimensional flow-field data to a low-dimensional (two- or three-dimensional) manifold, enabling highly accurate prediction of pressure distribution for new shapes. By fully exploiting the inherent low-dimensional manifold of the flow field, the proposed framework enables highly efficient and accurate optimization. Most notably, the entire optimization process completes in mere minutes, conclusively demonstrating the framework's exceptional computational efficiency and precision.