Deep Gaussian process for enhanced Bayesian optimization and its application in additive manufacturing

Raghav Gnanasambandam, Bo Shen, Andrew Chung Chee Law, Chaoran Dou and Zhenyu (James) Kong

IISE Transactions, 2025, vol. 57, issue 4, 423-436

Abstract: 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 non-stationary functions. Several analytical test functions and a case study in metal AM simulation demonstrate the applicability of the proposed method.

Date: 2025
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DOI: 10.1080/24725854.2024.2312905

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