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On the Use of Symmetries in Building Surrogate Models

[+] Author and Article Information
M. Giselle Fernandez-Godino

Ph.D. Candidate, Student Member of ASME, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, United States
gisellefernandez@ufl.edu

S. Balachandar

William F. Powers Professor, Fellow of ASME, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, United States
bala1s@ufl.edu

Raphael Haftka

Distinguished Professor, Fellow of ASME, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, United States
haftka@ufl.edu

1Corresponding author.

ASME doi:10.1115/1.4042047 History: Received May 04, 2018; Revised October 01, 2018

Abstract

When simulations are expensive and multiple realizations are necessary, as is the case in uncertainty propagation, statistical inference and optimization, surrogate models can achieve accurate predictions at low computational cost. In this paper, we explore options for improving the accuracy of a surrogate if the modeled phenomenon presents symmetries. These symmetries allow us to obtain free information and, therefore, the possibility of more accurate predictions. We present an analytical example along with a physical example that present parametric symmetries. Although imposing parametric symmetries in surrogate models seems to be a trivial matter, there is not a single way to do it and, furthermore, the achieved accuracy might vary. We present different ways of imposing symmetry in surrogate models. The performance of the options was compared with 100 random design of experiments where symmetries were not imposed. We found that each of the options to include symmetries performed the best in one or more of the studied cases and, in all cases, the errors obtained imposing symmetries were substantially smaller than the worst cases among the 100. We explore the options for using symmetries in two surrogates that present different challenges and opportunities: Kriging and linear regression. Kriging is often used as a black box, therefore we consider approaches to include the symmetries without changes in the main code. On the other hand, since linear regression is often built by the user owing to its simplicity we consider also approaches that modify the linear regression basis functions to impose the symmetries.

Copyright (c) 2018 by ASME
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