Uncertainty Propagation via Probability Measure Optimized Importance Weights with Application to Parametric Materials Models

摘要

This work proposes a least squares formulation to determine a set of empirical importance weights to achieve a change of probability measure. The objective is to estimate statistics from a target distribution using random samples generated from a different proposal distribution. The approach taken here works directly with the probability measure of the proposal and target distributions, for which only samples from each are needed. The result is an approach more capable of achieving high dimensional probability measure change than current state-of-the-art. Such a method can enable efficient and accurate propagation of uncertainty through model chains of unknown input and output regularity, such as those often encountered in process-structure-property chains in materials science. The proposed approach is demonstrated on four benchmark problems of increasing dimension and a Johnson-Cook model problem.