Toward Consistent Data Assimilation with Structured Generative Models

Abstract:

Accurate state estimation, also known as data assimilation, is essential for geophysical forecasts, ranging from numerical weather prediction to long-term climate studies.  While ensemble Kalman methods are widely adopted for this task in high-dimensional settings, these methods are inconsistent in capturing true uncertainty in non-Gaussian settings.  This presentation introduces a framework for consistent data assimilation.  First, inference methods based on conditional generative models are shown to generalize ensemble Kalman methods and to better characterize both the state and its associated uncertainty in nonlinear filtering problems.  Second, a dimension-reduction approach for limited-data settings is presented by identifying and encoding low-dimensional structure in generative models, with guarantees on approximation error.  The benefits of this framework are demonstrated through applications in fluid mechanics involving chaotic dynamics, where classical methods exhibit instability in small-sample regimes.

Speaker’s Bio:

Dr. Ricardo Baptista is an Assistant Professor in Statistical Sciences at the University of Toronto and a Faculty Affiliate at the Vector Institute.  His research focuses on establishing the mathematical foundations and theoretical guarantees of probabilistic machine learning models, with broad applications in science and engineering.  Before joining the University of Toronto, he served as an Instructor in Computing and Mathematical Sciences at California Institute of Technology, and as a Postdoctoral Scientist at Amazon.  He holds a Ph.D. in Computational Science and Engineering from the Massachusetts Institute of Technology, where he specialized in uncertainty quantification, and a Bachelor of Applied Science in Engineering Science from the University of Toronto.