Nathan Glatt-Holtz : A Bayesian approach to quantifying uncertainty in divergence free flows

Posted by Mimi Dai , part of the Analysis and Applied Mathematics Seminar.

At

April 26, 2021, 4 p.m.

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Abstract

We treat a statistical regularization of the ill-posed inverse problem of estimating a divergence free flow field $u$ from the partial and noisy observation of a passive scalar $\theta$ which is advected by $u$. Our solution is a Bayesian posterior distribution, that is a probability measure $\mu$ of the space of divergence free flow fields which precisely quantifies uncertainties in $u$ once one specifies models for measurement error and a prior knowledge for $u$. In this talk we survey some of our recent work which analyzes $\mu$ both analytically and numerically. In particular we discuss a posterior contraction (consistency) result as well as some Markov Chain Monte Carlo (MCMC) algorithms which we have developed, refined and rigorously analyzed to effectively sample from $\mu$. This is joint work with Jeff Borggaard, Justin Krometis and Cecilia Mondaini.