A comparison of numerical optimizers in developing high dimensional surrogate models

Yanwen Xu, Pingfeng Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publication45th Design Automation Conference
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791859193
DOIs
StatePublished - Jan 1 2019
EventASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019 - Anaheim, United States
Duration: Aug 18 2019Aug 21 2019

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume2B-2019

Conference

ConferenceASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019
CountryUnited States
CityAnaheim
Period8/18/198/21/19

Keywords

  • High dimension
  • Maximum Likelihood Estimation
  • Surrogate Model

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

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