Surrogate modeling: tricks that endured the test of time and some recent developments

Abstract

Tasks such as analysis, design optimization, and uncertainty quantification can be computationally expensive. Surrogate modeling is often the tool of choice for reducing the burden associated with such data-intensive tasks. However, even after years of intensive research, surrogate modeling still involves a struggle to achieve maximum accuracy within limited resources. This work summarizes various advanced, yet often straightforward, statistical tools that help. We focus on four techniques with increasing popularity in the surrogate modeling community: (i) variable screening and dimensionality reduction in both the input and the output spaces, (ii) data sampling techniques or design of experiments, (iii) simultaneous use of multiple surrogates, and (iv) sequential sampling. We close the paper with some suggestions for future research.

URBaM: A Novel Surrogate Modelling Method to Determine Design Scaling Rules for Product Families

“…The URBaM modelling technique is based on the use of full factorial DOEs, which are not recommended to be used with more than 5 design variables, as reported by F. A. Viana et al (2021). Therefore, the authors of the present work recommend limiting below that value the maximum number of design variables considered to build the surrogate model.…”

Research on Applicability and Efficient Construction with Typical Surrogate Models

“…Surrogate model (SM) is also known as meta-model, it simulates the characteristics of the entire system with lower computational cost [1][2]. For more than 40 years, SMs have been widely used in engineering optimization and quantification of uncertainty for improving efficiencies [3]. Nowadays, to determine a satisfactory SM and the number of experimental samples, it is still a topic worthy for discussing continuously, because it is seriously related to the quality of optimization design and the cost of real evaluation [4].…”

“…The construction of SM based on design of experiment (DOE) depends on the real samples, and evaluating these samples are reasonably time-consuming. In practice, the variable number and the surrogate order are the main consideration for constructing SM, and the count of the real evaluations rises quickly as the count of variables increases [3]. Therefore, to reduce the cost budget, it is of great significance to study the predicted performances of the SMs under a limited real samples.…”

A Vine Copula‐Based Polynomial Chaos Framework for Improving Multi‐Model Hydroclimatic Projections at a Multi‐Decadal Convection‐Permitting Scale

“…Monte Carlo (MC) simulation is one of the most widely used uncertainty analysis techniques but is quite time‐consuming since a great number of model simulations are required for accurate estimates (Maina & Siirila‐Woodburn, 2020; Tran et al., 2020; J. Zhang et al., 2020). To overcome this problem, a simpler representation of physical models has been investigated through various surrogate techniques (Bass & Bedient, 2018; Razavi et al., 2012; Viana et al., 2021), among which polynomial chaos expansion (PCE) has gained popularity due to its ability to efficiently estimate the effects of parameter uncertainty on model outputs (Hu et al., 2019; Man et al., 2019; H. Wang et al., 2020). PCE acts as a computationally efficient surrogate model in which the variability of the output is represented by the ensemble of the expansion coefficient.…”