## Modeling and Analysis of Dynamic Computer Experiments

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##### Date

##### Authors

Zhang, Ru

##### Keyword

Computer Experiments , Gaussian Process , Inverse Problem , Singular Value Decomposition , Time Series

##### Abstract

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.