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

Raghav Gnanasambandam, Bo Shen, Andrew Chung Chee Law, Chaoran Dou, Zhenyu Kong

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


ABSTARCT: 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.

Original languageEnglish (US)
JournalIISE Transactions
StateAccepted/In press - 2024

All Science Journal Classification (ASJC) codes

  • Industrial and Manufacturing Engineering


  • additive manufacturing
  • bootstrap aggregation
  • deep Gaussian process
  • surrogate modeling
  • “Black-box” functions


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