Bayesian optimization using deep Gaussian processes with applications to aerospace system design

Bayesian Optimization using Gaussian Processes is a popular approach to deal with optimization involving expensive black-box functions. However, because of the assumption on the stationarity of the covariance function defined in classic Gaussian Processes, this method may not be adapted for non-stat...

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Bibliographic Details
Published inOptimization and engineering Vol. 22; no. 1; pp. 321 - 361
Main Authors Hebbal, Ali, Brevault, Loïc, Balesdent, Mathieu, Talbi, El-Ghazali, Melab, Nouredine
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2021
Springer Nature B.V
Springer Verlag
Subjects
Aerospace engineering
Aerospace systems
Bayesian analysis
Control
Covariance
Design optimization
Engineering
Environmental Management
Financial Engineering
Gaussian process
Machine Learning
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Optimization and Control
Research Article
Statistics
Systems design
Systems Theory
Gaussian process
Non-stationary function
Bayesian optimization
Deep Gaussian process
Global constrained optimization
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Summary:Bayesian Optimization using Gaussian Processes is a popular approach to deal with optimization involving expensive black-box functions. However, because of the assumption on the stationarity of the covariance function defined in classic Gaussian Processes, this method may not be adapted for non-stationary functions involved in the optimization problem. To overcome this issue, Deep Gaussian Processes can be used as surrogate models instead of classic Gaussian Processes. This modeling technique increases the power of representation to capture the non-stationarity by considering a functional composition of stationary Gaussian Processes, providing a multiple layer structure. This paper investigates the application of Deep Gaussian Processes within Bayesian Optimization context. The specificities of this optimization method are discussed and highlighted with academic test cases. The performance of Bayesian Optimization with Deep Gaussian Processes is assessed on analytical test cases and aerospace design optimization problems and compared to the state-of-the-art stationary and non-stationary Bayesian Optimization approaches.
ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-020-09517-8