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Project

Computational methods for high-dimensional Bayesian inverse problems with full-field Data.

In this proposal, we will develop particle methods for sampling and optimization in computationally challenging Bayesian inverse problems. We will consider problems that are modeled by a (possibly high-dimensional) PDE that describes evolution of a system in space, time and potentially contains additional degrees of freedom. In this model, we need to estimate unknown parameters that are potentially infinite-dimensional (e.g., a function of space), based on measurement high-resolution measurement data. The main objectives of this proposal are three-fold. We will increase reliability of the computed Bayesian posterior distributions quantifying and reducing bias due to model error, and by quantifying uncertainty due to noisy measurement data. We will moreover increase efficiency of computation by exploiting their multilevel/multiscale structure in the computational framework. Finally, we will establish a link between Bayesian inverse problems and deep learning, opening an additional path towards explainable AI.

Date:1 Oct 2023 →  Today
Keywords:Multilevel/multiscale methods, Bayesian inverse problems, Uncertainty quantification
Disciplines:Numerical computation, Numerical analysis