Modeling and Analysis of Dynamic Computer Experiments

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Zhang, Ru
Computer Experiments , Gaussian Process , Inverse Problem , Singular Value Decomposition , Time Series
Dynamic computer experiments which refer to computer experiments with time series outputs have increasingly gained popularity in both science and engineering. Analysis of dynamic computer experiments through statistical emulators or surrogate models emerges as an important topic in statistical literature. This thesis is devoted to three research topics in modeling and analysis of dynamic computer experiments. We propose new methodologies for (a) efficient inference of Gaussian process models for large-scale dynamic computer experiments; (b) the inverse problem for small-scale dynamic computer experiments, that is, when a target response is available, we aim to estimate the inputs of the computer simulator that produce a response matching the target as closely as possible; (c) the inverse problem in large-scale dynamic computer experiments, which requires fitting the Gaussian process emulator efficiently given a large input data set to obtain the estimated solution to the inverse problem. For the large-scale dynamic computer experiments, we propose a local approximate singular value decomposition based Gaussian process (lasvdGP) model, which is shown to provide accurate and efficient emulation for the dynamic computer simulator. For the small-scale inverse problem, we introduce a sequential design approach which selects follow-up design points as per a proposed expected improvement criterion. The effectiveness of this approach is verified by both the theoretical study of convergence and the empirical study compared with existing alternative methods. For the inverse problem in large-scale dynamic computer experiments, we propose an approximate Bayesian inference algorithm using the proposed lasvdGP model. This approach gives promising results to address the computational challenge of the large input data set of the dynamic computer simulator.
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