Invited talk by Bruno Sudret

More information on the workshop can be found external pageherecall_made.

Abstract

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. These so-called simulators 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, model calibration/inversion or optimal design problems would require thousands to millions of runs with different values of the model input parameters, which is not affordable with high-fidelity, costly simulators.

Polynomial chaos expansions (PCE) have emerged two decades ago to solve partial differential equations with random coefficients [1]. In the last decade, with the development of so-called non intrusive methods [2], they have become a mature tool for building surrogate models of complex simulators, which is nowadays applied in civil, mechanical and electrical engineering but also in economics, and recently in astrophysics. Sparse PCE, which are based on statistical learning and compressive sensing approaches nowadays allow to use PCEs also in high-dimensions [3].

In this talk, the basic machinery of PCEs will be presented, as well algorithms to compute sparse expansions at low cost (typically, a few dozens to hundreds of runs of the original model, for problems with up to 100 parameters). These sparse PCEs allow for the most efficient computation of the well-established Sobol’ (global) sensitivity indices, but can also be use in the context of Bayesian model calibration and rare event estimation. Application to subsurface flow [4] and other engineering problems will be presented as an illustration.

[1] Ghanem, R. & Spanos, P. (2003) Stochastic Finite Elements: A Spectral Approach, Courier Dover Publications, Mineola.
[2] Berveiller, M., Sudret, B. & Lemaire, M. (2006) Stochastic finite elements: a non-intrusive approach by regression, Eur. J. Comput. Mech., 15, pp. 81-92.
[3] Blatman, G. & Sudret, B. (2011) Adaptive sparse polynomial chaos expansion based on Least Angle Regression, J. Comput. Phys, 230, pp. 2345-2367.
[4] Deman, G., Konakli, K., Sudret, B., Kerrou, J., Perrochet, P. & Benabderrahmane, H. (2016) Using sparse polynomial chaos expansions for the global sensitivity analysis of groundwater lifetime expectancy in a multi-layered hydrogeological model, Reliab. Eng. Sys. Safety, 147, pp. 156-169.