Deep Gaussian Process for Enhanced Bayesian Optimization and its Application in Additive Manufacturing

Engineering design problems typically require optimizing a quality measure by finding the right combination of controllable input parameters. In additive manufacturing (AM), the output characteristics of the process can often be non-stationary functions of the process parameters. Bayesian Optimization (BO) is a methodology to optimize such “black-box” functions, i.e., the input-output relationship is unknown and expensive to compute. Optimization tasks involving “black-box” functions widely use BO with Gaussian Process (GP) regression surrogate model. Using GPs with standard kernels is insufficient for modeling non-stationary functions, while GPs with non-stationary kernels are typically over-parameterized. On the other hand, a Deep Gaussian Process (DGP) can overcome GPs’ shortcomings by considering a composition of multiple GPs. Inference in a DGP is challenging due to its structure resulting in a non Gaussian posterior, and using DGP as a surrogate model for BO is not straightforward. Stochastic Imputation (SI) based inference is promising in speed and accuracy for BO. This work proposes a bootstrap aggregation based procedure to effectively utilize the SI-based inference for BO with a DGP surrogate model. The proposed BO algorithm DGP-SI-BO is faster and empirically better than the state-of-the-art BO method in optimizing nonstationary functions. Several analytical test functions and a case study in metal additive manufacturing simulation demonstrate the applicability of the proposed method.