Introducing latent variables in polynomial chaos expansions to surrogate stochastic simulators

Authors

X. Zhu, B. Sudret

Abstract

Stochastic simulators are computational models that produce different results when evaluated repeatedly with the same input parameters. In this respect, the model response conditional on the input is a random variable, and thus it is necessary to run the model many times to fully characterize the associated response. Due to the large number of necessary model runs, performing uncertainty quantification or optimization of a costly stochastic simulator is intractable directly. To alleviate the computational burden, we extend polynomial chaos expansions to metamodeling the entire response probability distribution of stochastic simulators. In this novel approach, we introduce a latent variable and an additional noise, on top of the well-defined input variables, to mimic the intrinsic stochasticity of the simulator. We develop a method to construct such a surrogate without requiring repeated runs of the simulator for the same input parameters. The performance of the proposed surrogate model is compared with one of the state-of-the-art kernel estimator on an analytical example from mathematical finance.