Surrogate models for uncertainty quantification: An overview

Uncertainty quantification has become a hot topic in computational sciences in the last decade. Indeed computer models (a.k.a simulators) are becoming more and more complex and demanding, yet the knowledge of the input parameters to feed into the model is usually limited. Based on the available data and possibly expert knowledge, parameters are represented by random variables. Of crucial interest is the propagation of the uncertainties through the simulator so as to estimate statistics of the quantities of interest. Monte Carlo simulation, a popular technique based on random number simulation, is unaffordable in practice when each simulator run takes minutes to hours. In this contribution we shortly review recent techniques to bypass Monte Carlo simulation, namely surrogate models. The basics of polynomial chaos expansions and low-rank tensor approximations are given together with hints on how to derive the statistics of interest, namely moments, sensitivity indices or probabilities of failure.