Past Event: Oden Institute Seminar

RESCHEDULED to Feb. 3 - The Mean-Field Ensemble Kalman Filter

Andrew Stuart, Professor, CalTech

Abstract

Ensemble Kalman filters constitute a methodology for incorporating noisy data into complex dynamical models to enhance predictive capability. They are widely adopted in the geophysical sciences, underpinning weather forecasting for example, and are starting to be used throughout the sciences and engineering; furthermore, they have been adapted to function as a general-purpose tool for parametric inference. The strength of these methods stems from their ability to operate using complex models as a black box, together with their natural adaptation to high performance computers. In this talk we introduce theory which, for the first time, elucidates conditions under which this widely adopted methodology provides accurate model predictions and uncertainties for discrete time filtering. The theory rests on a mean-field formulation of the methodology and an error analysis controlling differences between probability measure propagation under the mean-field model and under the true filtering distribution.

The mean-field formulation is based on joint work with Edoardo Calvello (Caltech) and Sebastian Reich (Potsdam).  The error analysis is based on joint work with Jose Carrillo (Oxford), Franca Hoffmann (Caltech) and Urbain Vaes (Paris).

 

 

 

Biography

Andrew Stuart obtained his undergraduate degree in Mathematics, from Bristol University in 1983, his PhD from the Oxford University Computing Laboratory in 1987 and was then a postdoc at MIT in the period 1987--1989. Before joining Caltech he held permanent positions at Bath University (1989--1992), Stanford University (1992--1999) and Warwick University (1999--2016). His research interests focus on computational applied mathematics; and in particular challenges presented by the age of information, such as the integration of data with mathematical models and the mathematics of machine learning.  He has been awarded the Leslie Fox Prize fo Numerical Analysis in 1989, the IPST Monroe Martin Prize in 1995, the Whitehead Prize from the London Mathematical Society in 2000, and the James Wilkinson Prize in Numerical Analysis and Scientific Computing (1997), the Germund Dahlquist Prize (1997) and the J.D. Crawford Prize (2007), all from SIAM.  He was elected an inaugural SIAM Fellow in 2009.  He delivered invited lectures at the International Congress of Industrial and Applied Mathematics (ICIAM) in 2007 and 2023, at the European Congress of Mathematicians (ECM) in 2012 and at the International Congress of Mathematicians (ICM) in 2014. He was elected as a Fellow of The Royal Society in 2023.

Stuart's research is focused on the development of foundational mathematical and algorithmic frameworks for the seamless integration of models with data. He works in the Bayesian formulation of inverse problems for differential equations, and in data assimilation for dynamical systems.