Recent developments on surrogate models for stochastic simulators

Abstract

Computational models, a.k.a. simulators, are used in all fields of engineering and applied sciences to help design and assess complex systems in silico. Advanced analyses such as optimization or uncertainty quantification, which require repeated runs by varying input parameters, cannot be carried out with brute force methods such as Monte Carlo simulation due to computational costs. Thus the recent development of surrogate models such as polynomial chaos expansions and Gaussian processes, among others. For so-called stochastic simulators used e.g.in epidemiology, mathematical finance or wind turbine design, there exists an intrinsic source of stochasticity on top of well-identified system parameters. As a consequence, for a given vector of inputs, repeated runs of the simulator (called replications) will provide different results, as opposed to the case of deterministic simulators. Consequently, for each input realization, the response is a random variable to be characterized. In this talk we present an overview of the literature devoted to building surrogate models of such simulators, which we call stochastic emulators. Then we focus on a recent approach based on generalized lambda distributions and polynomial chaos expansions. The approach can be used with or without replications, which brings efficiency and versatility. As an outlook, practical applications to sensitivity analysis will also be presented.