Seminars & Colloquia Calendar

Abstract:  In this talk I will argue that blending available scientific models with data is not only of great applied interest, but also a rich source of mathematical questions. I will first describe three classes of problems: data assimilation, Bayesian inverse problems, and semi-supervised learning. Then I will demonstrate the richness of mathematical ideas involved in the theoretical foundations and in the computational approach to these problems. In particular my research has made of use of tools from control theory, chaotic dynamical systems, large deviations for diffusions, regularity theory of fractional PDEs, divergences between probability measures, gamma-convergence, optimal transport and gradient flows, spectral analysis of graph-Laplacians, ergodic theory of Markov chains in infinite dimensional spaces, and numerical analysis. I will conclude with a summary of current and future directions of research.