Surrogate models for forward and inverse uncertainty quantification

Abstract

Computational models are used in virtually all fields of applied sciences and engineering to predict the behaviour of complex natural or man-made systems. Also known as simulators, they allow the analyst to assess the performance of a system in-silico, and then optimize its design or operating. High-fidelity models such as finite element models usually feature tens of parameters and are costly to run, even when taking full advantage of the available computer power. In parallel, the more complex the system, the more uncertainty in its governing parameters, environmental and operating conditions. In this respect, uncertainty quantification methods may require thousands to millions of model runs when using brute force techniques such as Monte Carlo simulation. In contrast, surrogate models (a.k.a. metamodels or emulators) allow one to tackle the problem by constructing an accurate approximation of the simulator’s response from a limited number of runs at selected values (the so-called experimental design) and some learning algorithm. In this lecture, we will first introduce surrogate models in general and show their links with supervised machine learning. We then present sparse polynomial chaos expansions and their application to global sensitivity analysis and dynamics. Finally the use of surrogate models for Bayesian inversion with and without Markov Chain Monte Carlo simulation will be presented.