Uncertainty quantification by PDE-based models
Over the past two decades, there has been a growing interest in enhancing the mathematical description of complex physical systems, by taking into account the often partial knowledge of the system itself or its instrinsic stochastic nature.
The group contributes to the development of advanced numerical techniques to both quantify how the uncertainty on the models propagates to certain quantities of interest, and address the challenge of making reliable decisions/designs under model uncertainties.
More specifically, the group develops advanced multi-level/index Monte Carlo methods for problems characterized by high-dimensional random parameters and low spatial regularity, modern stochastic optimization algorithms to minimize suitable risk-measures of random functionals, and surrogates based on Gaussian processes.
Another key interest lies in problems with a low regularity of the so-called ``parameter to solution" map, for which the group explores the combination of polynomial surrogates with machine learning techniques. Applications are numerous and vary from discrete fracture networks to wave energy converters and to quantum systems.