A method to efficiently localize non-dominated regions using surrogate modeling with multi-fidelity data from a sequenti
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RESEARCH PAPER
A method to efficiently localize non-dominated regions using surrogate modeling with multi-fidelity data from a sequential decision process Jaskanwal P. S. Chhabra1 · Gordon P. Warn1 Received: 2 June 2019 / Revised: 1 October 2019 / Accepted: 16 October 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract In recent studies, it has been shown that models of increasing fidelity can be used in a sequence to efficiently filter out dominated designs from a set of discrete designs under consideration by formally viewing design as a sequential decision process (SDP). In the SDP, efficiency is achieved by first using low-fidelity models to construct bounds on decision criteria that are used to filter out dominated design(s) having only performed inexpensive model evaluations, and then higher-fidelity evaluations are performed to precisely evaluate the decision criteria but only for the candidate design(s) that appear to be promising after the lower-fidelity evaluations. In this paper, a method is presented to leverage the information gained in the SDP for the efficient construction of a surrogate model with high accuracy in non-dominated regions. More specifically, a surrogate modeling method using Gaussian process regression is constructed using a composite data set—exact values of decision criteria obtained by the highest-fidelity evaluation, and bounded values of the decision criteria obtained by lowfidelity evaluations—generated by sequentially evaluating a set of discrete design alternatives using a set of multi-fidelity models to generalize across a continuous design domain. The result is a surrogate model that is highly accurate in the nondominated region(s) of the design domain, and yet captures the trend of the underlying objective function over the complete design domain without performing expensive model evaluations in regions that are not promising. The utility of the surrogate modeling method is illustrated through two applications. Keywords Design exploration · Multi-fidelity modeling · Gaussian process · Reinforcement learning · Sequential decision process
1 Introduction Surrogate models are commonly used for design exploration and optimization by generalizing across large design spaces when the computational cost of evaluating designs with high-fidelity model based simulation is computationally prohibitive. This generalization is accomplished using the outcome of sparse deterministic computer experiments in conjunction with statistics based models such as Response surfaces, Gaussian processes, Neural networks, among others (Sacks et al. 1989; Simpson et al. 2001b). Responsible Editor: Raphael Haftka Gordon P. Warn
[email protected] 1
The Pennsylvania State University, University Park, PA 16802, USA
More specifically, developing a surrogate model typically includes the analyst choosing an appropriate experimental design and sparsely sampling the broad design space, evaluating the sampled designs using high-fidelity computer simulations, choosing an appropriate statistical
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