Auto-differentiable Ensemble Kalman Filters

Daniel Sanz-Alonso (University of Chicago)

Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is particularly challenging when the state is high-dimensional and the state-space dynamics are unknown. In this talk I will introduce a machine learning framework for learning dynamical systems in data assimilation. Our auto-differentiable ensemble Kalman filters (AD-EnKFs) blend ensemble Kalman filters for state recovery with machine learning tools for learning the dynamics. In doing so, AD-EnKFs leverage the ability of ensemble Kalman filters to scale to high-dimensional states and the power of automatic differentiation to train high-dimensional surrogate models for the dynamics. Numerical results using the Lorenz-96 model show that AD-EnKFs outperform existing methods that use expectation-maximization or particle filters to merge data assimilation and machine learning. In addition, AD-EnKFs are easy to implement and require minimal tuning. This is joint work with Yuming Chen and Rebecca Willett.

Prof. Sanz-Alonso is an Assistant Professor in the Department of Statistics at the University of Chicago, and a member of the Committee on Computational and Applied Mathematics. His research addresses theoretical and compuational challenges motivated by data-centric applications in graph-based learning, inverse problems, and data assimilation. His work was recognized with the José Luis Rubio de Francia prize to the best Spanish mathematician under 32 by the Spanish Royal Society of Mathematics. Prof. Sanz-Alonso's research is funded by the National Science Foundation, the National Geospatial-Intelligence Agency, the Department of Energy, and the BBVA Foundation.

Before moving to Chicago, Prof. Sanz-Alonso was a postdoctoral research associate and a member of the Data Science Initiative at Brown University. He completed his Ph.D. in Mathematics and Statistics at the University of Warwick, UK.