A scalable composite Bayesian optimization framework for engineering design using deep learning reduced-order models

Composite Bayesian optimization (CBO) methods are attractive methods for black-box optimization problems. Though CBO methods offer significant benefits, extending CBO to high-dimensional input and output spaces has been less explored. The limited scalability and accuracy of multi-output Gaussian process (GP) models makes them less attractive for engineering design problems. Standard neural network-based models provide an alternative, but require the implementation of expensive and complex uncertainty quantification methods to enable CBO. As such, this paper develops Bayesian optimization using non-intrusive reduced-order models (ROMBO), a framework for high-dimensional CBO using deep learning reduced-order models. The framework utilizes autoencoders to create a nonlinear embedding of the output space that is modeled using a multi-task GP model. A Monte Carlo expected improvement acquisition function is used to balance exploration of the design space and exploitation of the composite objective function. The proposed framework is characterized using three synthetic problems and an inverse design problem for a transonic airfoil. It is compared with a standard BO implementation and a CBO implementation that generates an embedding of the outputs using proper orthogonal decomposition (POD). The results demonstrate that the ROMBO framework can achieve up to one to four orders of magnitude lower objective function values as compared to the other two methods. Additionally, ROMBO is more sample efficient than the other two methods, achieving far lower objective function values in fewer sampling iterations. This work demonstrates that ROMBO is a promising framework for enabling the use of CBO for complex high-dimensional design problems.