Bio: Youssef Marzouk is an associate professor in the Department of Aeronautics and Astronautics at MIT, and co-director of the MIT Center for Computational Engineering. He is also director of MIT’s Aerospace Computational Design Laboratory.

His research interests lie at the intersection of physical modeling with statistical inference and computation. In particular, he develops methodologies for uncertainty quantification, inverse problems, large-scale Bayesian computation, and optimal experimental design in complex physical systems. His methodological work is motivated by a wide variety of engineering, environmental, and geophysics applications.

He received his SB, SM, and PhD degrees from MIT and spent several years at Sandia National Laboratories before joining the MIT faculty in 2009. He is a recipient of the Hertz Foundation Doctoral Thesis Prize (2004), the Sandia Laboratories Truman Fellowship (2004-2007), the US Department of Energy Early Career Research Award (2010), and the Junior Bose Award for Teaching Excellence from the MIT School of Engineering (2012). He is an Associate Fellow of the AIAA and currently serves on the editorial boards of the SIAM Journal on Scientific Computing, Advances in Computational Mathematics, and the SIAM/ASA Journal on Uncertainty Quantification. He is also an avid coffee drinker and classical pianist.

A TOUR OF TRANSPORT METHODS FOR BAYESIAN COMPUTATION

Bayesian inference provides a natural framework for quantifying uncertainty in parameter estimates and model predictions, and for combining heterogeneous sources of information. Characterizing the results of Bayesian inference—by simulating from the posterior distribution—often proceeds via Markov chain Monte Carlo or sequential Monte Carlo sampling, but remains computationally challenging for complex posteriors and large-scale models.

This talk will describe a broad framework for using measure transport in Bayesian computation. This framework seeks deterministic couplings of the posterior measure with a tractable “reference” measure (e.g., a standard Gaussian). Such couplings are induced by transport maps, and enable direct simulation from the desired measure simply by evaluating the transport map at samples from the reference. Approximate transports can also be used to “precondition” and accelerate standard Monte Carlo schemes. Within this framework, one can describe many useful notions of low-dimensional structure associated with inference: for instance, sparse or decomposable transports underpin modeling and computation with non-Gaussian Markov random fields, and low-rank transports arise frequently in inverse problems.

We will then describe recent work specializing transport maps to the problem of nonlinear filtering in high-dimensional state-space models. The idea is to transform a forecast ensemble into samples from the current filtering distribution via a sequence of nonlinear transport maps, computed via convex optimization. Construction of the maps is regularized by leveraging potential structure in the filtering problem—e.g., decay of correlations, approximate conditional independence, and local likelihoods—thus extending notions of localization to nonlinear updates. The proposed framework can be understood as a non-Gaussian generalization of the ensemble Kalman filter.

This is joint work with Alessio Spantini, Daniele Bigoni, Ricardo Baptista, and Matthew Parno.

Prof. Marzouk is being hosted by Prof. Duraisamy (Aerospace). If you would like to meet him during his visit please send an email to [email protected]. If you are an MICDE student and would like to join Prof. Marzouk for lunch please RVSP here by Friday, November 30.