Gaussian process emulators for dynamical systems with random parameters
Diaz De la O, F. A. and Adhikari, S.
Tenth International Conference on Structural Safety and Reliability (ICOSSAR'09),
Osaka, Japan, September 2009.
Complex engineering systems are studied using computer codes (also
known as simulators) which might be very expensive to run. An
increasingly common solution is to employ a less expensive surrogate
model to investigate these systems. One possibility is to construct
a statistical approximation to the simulator, known as
Gaussian process emulator. Such technology is based on the
analysis and design of computer experiments (Satner et
al. and Sacks et al.), and on concepts of
Bayesian statistics. Using this approach, it is possible to
efficiently make inference about unknown output values by evaluating
a fairly limited number of carefully selected points in the input
domain of the simulator.
Gaussian process emulators work in the following way: A small set of
code runs is treated as training data used to update the prior
beliefs about the simulator. Such prior beliefs take the form of a
Gaussian stochastic process distribution. After conditioning on the
training runs and updating this prior distribution, the mean of the
resulting posterior distribution approximates the output of the
simulator at any untried input, whereas it reproduces the known
output of the simulator at each initial input.
This paper compares two strategies for selecting points to run a
simulator of the mean frequency response of a dynamical system with
random parameters, taking Monte Carlo simulation as a benchmark. The
input domain of the simulator is divided into two subdomains: the
one corresponding to the frequency domain and the one associated
with the random nature of the response. The results obtained confirm
that emulation is less computationally expensive than Monte Carlo
simulation. More importantly, the comparison of selection strategies
helps elucidate whether the accuracy and computation time of
Gaussian process emulators can be improved.
BiBTeX Entry
@INPROCEEDINGS{cp67,
AUTHOR={F. A. DiazDelaO and S. Adhikari},
TITLE={Gaussian process emulators for dynamical systems with random parameters},
BOOKTITLE={Tenth International Conference on Structural Safety and Reliability (ICOSSAR'09)},
YEAR={2009},
Address={Osaka, Japan},
Month={September}
}
by Sondipon Adhikari