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Surrogate modeling and model selection in irreducible high dimensions with small sample size

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Authors

Bhaduri, Anindya; Graham-Brady, Lori; Shields, Michael D.

Issue Date
2019-05-26
Citation
13th International Conference on Applications of Statistics and Probability in Civil Engineering(ICASP13), Seoul, South Korea, May 26-30, 2019
Abstract
There exist a number of high dimensional problems in which the dimensions cannot be effectively reduced, since all of them are more or less equally important. On top of that, when the computational models are expensive, it is not practical to perform more than a small number of model evaluations. In situations like this, a good space filling design is needed that provides maximum coverage over the input domain. In surrogate modeling methods, like kriging interpolation or radial basis function interpolation, a good sampling design can help improve the condition number of the kernel matrix by placing samples as far apart from each other as possible. In this study, the performance of three hierarchical space filled designs, namely Refined Latinized Stratified Sampling (RLSS), Hierarchical Latin Hypercube Sampling (HLHS) and Sobol quasi-random sequence, are compared using the Rosenbrock function in different dimensions. Ordinary kriging interpolation is chosen as the surrogate modeling method with different choices of correlation functions. The AIC criterion is used for model selection and the accuracy of selection is cross-verified using the root mean squared (RMS) error values.
Language
English
URI
https://hdl.handle.net/10371/153506
DOI
https://doi.org/10.22725/ICASP13.385
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