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Modeling Multivariate Simulator Outputs with Applications to Prediction and Sequential Pareto Minimization

Chen, Po-Hsu
http://rave.ohiolink.edu/etdc/view?acc_num=osu1469094583

Abstract Details

2016, Doctor of Philosophy, Ohio State University, Statistics.
A deterministic computer simulator is a mathematical representation of a physical system. The use of computer simulators to study physical systems has become increasingly popular when physical experiments are infeasible, expensive, or time consuming. However, many computer simulators are biased due to the simplified biology or physics employed. In such situations, when both physical observations and simulator data are available, calibration can be used to align the behavior of a simulator output with that of a target physical system. Calibration can be performed if the simulator has inputs that represent unknown constants in the physical system as well as common controllable inputs. The first research topic uses independent calibrated simulators to simultaneously optimize multiobjective functions. Here, optimization is used in the sense of Pareto because conflicting multiobjective functions need not have a common optimizer. This research introduces a sequential method for determining the Pareto Front of a multi-output physical system using a calibrated simulator. When additional physical observations can be taken sequentially, a minimax fitness (improvement) function to guide the search for the next vector of control input settings is proposed. Based on a Bayesian calibrated model, this method maximizes the posterior expected improvement function over untried control inputs. Alternatively, if the additional runs can only be made by using a computer simulator, the control input is chosen as above, and calibration parameters are selected to minimize the sum of the posterior mean square prediction errors. This methodology spreads points on the Pareto Front and, when the simulator is biased, it is much more efficient compared to simulator-only methods. Here, efficiency is measured using the hypervolume indicator function of the estimated Pareto Front, and the sequential procedure is shown to perform well through examples from the literature. A challenging problem in computer experiments is to model dependent multi-output computer simulators. The second research topic uses multivariate Gaussian process (GP) models to provide rapidly-computable, interpolating emulators of the output from simulator codes. In this work, new interpolating multivariat} GP models are proposed, denoted as VPGP, which have the potential to give good predictions of multivariate output having non-constant associations over the input space. The VPGP model uses a linear function of inputs in the cross-covariance matrix. This structure facilitates flexible modeling of the between-output dependencies. A constraint which can increase the estimation accuracy of the covariance of those points on the approximate Pareto Front is also proposed. The VPGP model with this constraint can be shown empirically to provide a better prediction of Pareto Front than competing models.
Thomas Santner (Advisor)
Angela Dean (Advisor)
Matthew Pratola (Committee Member)
293 p.
Statistics

Recommended Citations

Citations

  • Chen, P.-H. (2016). Modeling Multivariate Simulator Outputs with Applications to Prediction and Sequential Pareto Minimization [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1469094583

    APA Style (7th edition)

  • Chen, Po-Hsu. Modeling Multivariate Simulator Outputs with Applications to Prediction and Sequential Pareto Minimization. 2016. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1469094583.

    MLA Style (8th edition)

  • Chen, Po-Hsu. "Modeling Multivariate Simulator Outputs with Applications to Prediction and Sequential Pareto Minimization." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1469094583

    Chicago Manual of Style (17th edition)

osu1469094583
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This open access ETD is published by The Ohio State University and OhioLINK.