Emulators for stochastic simulation codes

TL;DR

This paper develops methods to create fast, accurate metamodels for stochastic simulation codes, focusing on modeling the entire output probability density function rather than just mean outputs.

Contribution

It introduces two approaches for building probabilistic metamodels of stochastic codes, including kernel regression and density decomposition methods, with applications to real-world cases.

Findings

Kernel regression effectively models output densities.

Density decomposition captures complex stochastic behaviors.

Methods are validated on industrial and analytical models.

Abstract

Numerical simulation codes are very common tools to study complex phenomena, but they are often time-consuming and considered as black boxes. For some statistical studies (e.g. asset management, sensitivity analysis) or optimization problems (e.g. tuning of a molecular model), a high number of runs of such codes is needed. Therefore it is more convenient to build a fast-running approximation - or metamodel - of this code based on a design of experiments. The topic of this paper is the definition of metamodels for stochastic codes. Contrary to deterministic codes, stochastic codes can give different results when they are called several times with the same input. In this paper, two approaches are proposed to build a metamodel of the probability density function of a stochastic code output. The first one is based on kernel regression and the second one consists in decomposing the output density on a basis of well-chosen probability density functions, with a metamodel linking the coefficients and the input parameters. For the second approach, two types of decomposition are proposed, but no metamodel has been designed for the coefficients yet. This is a topic of future research. These methods are applied to two analytical models and three industrial cases.