RT Journal Article
ID 4f2e4f3e3689e792
A1 Dalbey, Keith R.
A1 Swiler, Laura P.
T1 GAUSSIAN PROCESS ADAPTIVE IMPORTANCE SAMPLING
JF International Journal for Uncertainty Quantification
JO IJUQ
YR 2014
FD 2014-04-17
VO 4
IS 2
SP 133
OP 149
K1 uncertainty quantification
K1 probability theory
K1 Monte Carlo
K1 mixture models
AB The objective is to calculate the probability, P_{F}, that a device will fail when its inputs, x, are randomly distributed with probability density, p (x), e.g., the probability that a device will fracture when subject to varying loads. Here failure is defined as some scalar function, y (x), exceeding a threshold, T. If evaluating y (x) via physical or numerical experiments is sufficiently expensive or P_{F} is sufficiently small, then Monte Carlo (MC) methods to estimate P_{F} will be unfeasible due to the large number of function evaluations required for a specified accuracy. Importance sampling (IS), i.e., preferentially sampling from "important" regions in the input space and appropriately down-weighting to obtain an unbiased estimate, is one approach to assess P_{F} more efficiently. The inputs are sampled from an importance density, p' (x). We present an adaptive importance sampling (AIS) approach which endeavors to adaptively improve the estimate of the ideal importance density, p* (x), during the sampling process. Our approach uses a mixture of component probability densities that each approximate p* (x). An iterative process is used to construct the sequence of improving component probability densities. At each iteration, a Gaussian process (GP) surrogate is used to help identify areas in the space where failure is likely to occur. The GPs are not used to directly calculate the failure probability; they are only used to approximate the importance density. Thus, our Gaussian process adaptive importance sampling (GPAIS) algorithm overcomes limitations involving using a potentially inaccurate surrogate model directly in IS calculations. This robust GPAIS algorithm performs surprisingly well on a pathological test function.
PB Begell House
LK http://dl.begellhouse.com/journals/52034eb04b657aea,14db5d4c2510c6cc,4f2e4f3e3689e792.html