Computationally Inexpensive Metamodel Assessment Strategies

By Martin Meckesheimer, A. Booker, Russell R. Barton, Timothy W. Simpson. 2002

348 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b16d40bb6237aef4c4188a0f85bb7c805b3ab7dc

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In Computational Theory and Mathematics

In Management Science and Operations Research

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Citations in the corpus

Efficient Pareto Frontier Exploration using Surrogate Approximations (2000, background): “Validation can be achieved through a variety of means, including residual error analysis (Myers and Montgomery, 1995) and cross-validation (Meckesheimer et al., 2001).”
Using Cross Validation to Design Conservative Surrogates (2010, methodology): “For unbiased surrogates, there has been research pointing to the utility of cross validation [24–29] for selecting the most accurate surrogate from several fitted surrogates.”
Metamodel based high-fidelity stochastic analysis of composite laminates: A concise review with critical comparative assessment (2017, methodology): “These are orthogonal arrays [52–54], Latin Hypercube designs [55–59], Hammersley sequences [60,61] and uniform designs [62].”
Multiple surrogates: how cross-validation errors can help us to obtain the best predictor (2009, methodology): “Lin et al. (2002) and Meckesheimer et al. (2002) presented an investigation on the use of cross-validation for RMSE estimation.”
A review on design, modeling and applications of computer experiments (2006, methodology): “In particular, Meckesheimer et al. (2001) and Meckesheimer et al. (2002) have applied the multi-quadratic RBF form to construct an approximation after Hardy (1971), who used linear combinations of a radially symmetric function based on the Euclidean distance of the form: where (cid:6) · (cid:6)…”
Predictive quantification of surrogate model fidelity based on modal variations with sample density (2015, methodology): “Meckesheimer et al. (2002) used the root mean square error of k-fold cross-validation (RMSECV), i.e., root mean square of PRESS (PRESSRMS), to measure the global accuracy of the surrogate over the entire design domain: RMSECV = √ √ √ √ 1 k k ∑ i=1 ( ŷi − ŷ(−i)i )2 (6) where k is the number of…”
Use of Kriging Models to Approximate Deterministic Computer Models (2005, methodology): “As a more computationally efficient alternative, cross-validation (CV) [2,47,48] or Akaike’s information criteria (AIC) can be used [49,50].”
Review of Metamodeling Techniques in Support of Engineering Design Optimization (2007, methodology): “[26, 85] studied the cross-validation method.”
Application-driven sequential designs for simulation experiments: Kriging metamodelling (2004, background): “Obviously, estimation of variogram ( 7 ) requires at least three different values of h (for example, the values 0, 1 2 ,1 );”
Approximation methods in multidisciplinary analysis and optimization: a panel discussion (2004, methodology): “A simplified procedure for leave-one-out cross validation of kriging models is presented by Mitchell and Morris (1992), but recent studies by Meckesheimer et al. (2002) found that leave-one-out cross validation does not work well for validating kriging models.”
Comparing error estimation measures for polynomial and kriging approximation of noise-free functions (2009, methodology): “ Meckesheimer et al. (2002) studied the influence of number of points in sub-samples to compute the generalized cross-validation error and gave their recommendations on sub-sample size to estimate GCV for different surrogates.”
Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions (2010, methodology): “Meckesheimer et al. (2002) investigated assessment methods for model validation based on leave-k-out cross validation.”
Metamodeling in Multidisciplinary Design Optimization: How Far Have We Really Come? (2014, background): “Research has improved the assessment of global accuracy [105,217] (most of the time, valid for any metamodeling technique).”