Seminar: Toward consistent nonlinear filtering and smoothing via measure transport

Speaker: Ricardo Baptista with Caltech

Abstract

Solving filtering and smoothing problems for geophysical applications involve estimating the hidden states of complex systems and accurately characterizing their uncertainty. Popular algorithms for tackling these problems include ensemble Kalman methods such as the EnKF, EnKS and RTS smoother. While these algorithms yield robust state estimates for high-dimensional models with non-Gaussian statistics, ensemble Kalman methods are limited by linear transformations and are generally inconsistent with the true Bayesian solution. In this presentation, I will discuss how measure transport can be used to consistently transform a prior ensemble into samples from a filtering or smoothing distribution. This approach provides a natural generalization of Kalman methods to nonlinear transformations, thereby reducing the intrinsic bias of classic algorithms with a marginal increase in computational cost. In small-sample settings, I will show how to estimate transport maps for high-dimensional inference problems by exploiting low-dimensional structure in the target distribution. Finally, I will demonstrate the benefit of this framework for filtering and smoothing on chaotic dynamical systems and aerodynamic flows.

Biography

Ricardo is a von Karman Instructor in Computing + Mathematical Sciences at Caltech where he is hosted by both Andrew Stuart and Houman Owhadi. Prior to Caltech, Ricardo received a PhD in 2022 from the Center for Computational Science and Engineering at MIT, where he was advised by Youssef Marzouk who leads a research group in uncertainty quantification. Ricardo's research focuses on developing methods for probabilistic modeling and Bayesian inference that are scalable to high-dimensional problems. Before his PhD, he received a BASc in Engineering Science from the University of Toronto and worked in Flight Sciences at Bombardier Aerospace.

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