Surrogating stochastic simulators from sample trajectories using a non-Gaussian random field approach

Abstract

Stochastic simulators are a class of computational models that give a different response each time they are run, even if the same input parameters are used. Such a simulator can be viewed as a random field, indexed by the space of its input parameters. We focus on a class of stochastic simulators for which it is possible to generate trajectories, i.e., evaluations of the simulator throughout the space of input parameters for which the latent variables that induce the stochasticity of the simulator are held fixed (e.g., by fixing the random seed). Stochastic simulators are typically highly complex and expensive to run, which makes uncertainty analysis and optimization costly. These costs can be alleviated by replacing the simulator with a suitable surrogate model, which captures the essential characteristics of the original model while being much cheaper to evaluate. We propose a surrogate model that combines sparse polynomial chaos expansion, extended Karhunen-Loève expansion, and parametric inference of joint distributions in the marginal-copula framework to represent the stochastic simulator based on a number of model evaluations. The resulting surrogate model has an analytical form that can easily be used to compute moments and to sample new trajectories. In this talk, we demonstrate the performance of our surrogate model on a real-world engineering application, and show how it can be utilized to perform conditional prediction.