Sequential Design and Metamodeling for Computer Experiments

Abstract

Computer simulation models are increasingly used to study complex engineering systems, but their high computational cost often limits the number of simulations that can be performed. This thesis develops sequential design strategies for efficient metamodeling of expensive computer simulations, with a particular focus on stochastic simulations exhibiting input-dependent noise. The proposed methods aim to improve predictive accuracy under limited simulation budgets while providing reliable uncertainty quantification.

The thesis begins with a motivating application in performance-based seismic design of wood-frame podium buildings. A Kriging metamodel with an adaptive sampling strategy is developed to efficiently approximate the relationship between structural design parameters and seismic response. The resulting surrogate is used to identify reliable design regions in which simplified seismic analysis procedures can be applied with high confidence.

Building on this application, the thesis develops a fully Bayesian sequential design framework for heteroscedastic stochastic simulation models. The proposed approach employs dual Gaussian process surrogates to jointly model the mean response and input-dependent noise, and introduces an expected Bayesian integrated mean squared prediction error (BIMSPE) criterion for sequential point selection. By fully propagating uncertainty in model parameters and latent noise through posterior inference and sequential importance sampling, the proposed method achieves improved predictive accuracy, noise estimation, and uncertainty quantification compared with existing empirical Bayes and variational approaches.

Finally, the thesis extends the fully Bayesian framework from one-at-a-time sequential design over a discrete candidate set to batch-sequential design over continuous input spaces. A computationally efficient two-step strategy is proposed that first generates promising candidate batches through continuous optimization of an analytical batch IMSPE reduction criterion and then performs a fully Bayesian reranking using an approximation to the expected BIMSPE criterion. This extension enables practical batch selection while preserving the advantages of fully Bayesian uncertainty quantification and leveraging parallel computing resources.

Extensive numerical studies on synthetic examples and a seismic engineering application demonstrate that the proposed methods consistently improve surrogate accuracy and uncertainty quantification while remaining computationally tractable. Collectively, this thesis advances Bayesian sequential design methodology for global metamodeling of expensive stochastic simulations and provides practical algorithms for modern simulation-based engineering applications.