TY - GEN
T1 - A comparison of numerical optimizers in developing high dimensional surrogate models
AU - Xu, Yanwen
AU - Wang, Pingfeng
N1 - Funding Information:
This research is partially supported by the National Science Foundation through the Faculty Early Career Development (CAREER) award (CMMI-1813111), and the NSF award (CMMI-1802489).
Publisher Copyright:
Copyright © 2019 ASME.
PY - 2019
Y1 - 2019
N2 - The Gaussian Process (GP) model has become one of the most popular methods to develop computationally efficient surrogate models in many engineering design applications, including simulation-based design optimization and uncertainty analysis. When more observations are used for high dimensional problems, estimating the best model parameters of Gaussian Process model is still an essential yet challenging task due to considerable computation cost. One of the most commonly used methods to estimate model parameters is Maximum Likelihood Estimation (MLE). A common bottleneck arising in MLE is computing a log determinant and inverse over a large positive definite matrix. In this paper, a comparison of five commonly used gradient based and non-gradient based optimizers including Sequential Quadratic Programming (SQP), Quasi-Newton method, Interior Point method, Trust Region method and Pattern Line Search for likelihood function optimization of high dimension GP surrogate modeling problem is conducted. The comparison has been focused on the accuracy of estimation, the efficiency of computation and robustness of the method for different types of Kernel functions.
AB - The Gaussian Process (GP) model has become one of the most popular methods to develop computationally efficient surrogate models in many engineering design applications, including simulation-based design optimization and uncertainty analysis. When more observations are used for high dimensional problems, estimating the best model parameters of Gaussian Process model is still an essential yet challenging task due to considerable computation cost. One of the most commonly used methods to estimate model parameters is Maximum Likelihood Estimation (MLE). A common bottleneck arising in MLE is computing a log determinant and inverse over a large positive definite matrix. In this paper, a comparison of five commonly used gradient based and non-gradient based optimizers including Sequential Quadratic Programming (SQP), Quasi-Newton method, Interior Point method, Trust Region method and Pattern Line Search for likelihood function optimization of high dimension GP surrogate modeling problem is conducted. The comparison has been focused on the accuracy of estimation, the efficiency of computation and robustness of the method for different types of Kernel functions.
KW - High dimension
KW - Maximum Likelihood Estimation
KW - Surrogate Model
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U2 - 10.1115/DETC2019-97499
DO - 10.1115/DETC2019-97499
M3 - Conference contribution
AN - SCOPUS:85076361857
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - 45th Design Automation Conference
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019
Y2 - 18 August 2019 through 21 August 2019
ER -