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