# Designing computer experiments to estimate integrated response functions

Abstract (Summary)

Complex physical systems can be modeled mathematically and then solved by
appropriate numerical methods implemented by a complex computer code. Such
computer codes allow us to construct analogs of physical experiments that would
not be possible due to physical, financial and/or time constraints. In a computer
experiment, a response, y(x), usually deterministic, is computed by the code for each
set of input variables, x, according to an experimental design strategy. Then, as in
physical experiments, the relationship between the inputs x and y(x) is studied.
We are concerned with the design of computer experiments when there are two
types of inputs x = (xc, xe): control variables that can be set by researcher or
product designer, xc, and environmental variables that are not controlled in the
field but have some probability distribution characterizing a population of interest,
xe. Our interest is in accurately predicting the mean of the deterministic response
function µ(xc) = E[y(xc, Xe)] over the distribution of the environmental variables.
We introduce a new method for constructing an “inexpensive” predictor of the mean
response that is of greatest use when the complexity of the computer code or the
high-dimensionality of inputs limit the number of runs possible and V ar[y(xc, Xe)]
varies considerably as xc varies. We also propose a sequential design strategy for
constructing the training data on which to base the predictor in such problems where
the variance of the response surface varies greatly over the control space. In such cases,
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all further computing effort is best spent taking more observations in the regions of
the control space where the variance appears higher. The procedures introduced
are illustrated by examples utilizing test functions from the numerical optimization
literature.
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Bibliographical Information:

Advisor:

School:The Ohio State University

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:computer simulation adaptive sampling statistics

ISBN:

Date of Publication: