Surrogate models for efficient 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 engineers to assess the performance of a system in-silico, and then optimize its design or operating. Realistic representations 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 used to solve reliability, sensitivity or optimal design problems may require thousands to millions of model runs when using brute force techniques such as Monte Carlo simulation, which is not affordable with high-fidelity simulators.In contrast, surrogate models allow us to tackle these problems 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, general features of surrogate models will be first introduced. Polynomial chaos expansions will then be discussed in details, together with their sparse version for high-dimensional problems. Recent extensions to dynamics will be addressed and applications in sensitivity will be shown as an illustration.