Surrogate modelling for uncertainty quantification in engineering applications
Computational models are used nowadays in virtually all fields of applied sciences and engineering to predict the behaviour of complex natural or man-made systems. Those simulators allow the analyst to assess the performance of systems before actual manufacturing. They usually feature dozens of parameters and are expensive to run, even when taking full advantage of the available computer power. In this respect, uncertainty quantification techniques used to solve reliability, sensitivity or optimal design problems usually require thousands to millions of runs with different values of the model input parameters, which is not affordable with high-fidelity, costly simulators. This has led to the development of surrogate models in the last decade. Surrogate models can be considered as accurate approximations of the underlying simulator built from a limited number of runs at selected values (the experimental design) and some learning algorithm. In this talk, an overview of the most efficient non-intrusive techniques for surrogate modelling will be given, namely polynomial chaos expansions (including sparse approaches for high-dimensional problems), Kriging (a.k.a. Gaussian process modelling), their combination into PC-Kriging, as well as low-rank tensor approximations. Recent extensions to dynamics problems will be addressed. Various applications in model calibration (Bayesian inversion), sensitivity and reliability analysis in civil and mechanical engineering will be presented as an illustration.