Abstract: Stability of nonlinear filters for deterministic dynamical systems – the most common situation for data assimilation in earth science applications – is an outstanding problem, which is the focus of this talk. I will first discuss some recent theoretical results proving filter stability for chaotic deterministic systems and how the properties of the filtering distributions are related to the instabilities of the dynamics. On the other hand, current numerical literature explores stability in terms of RMSE which, although practical, cannot represent the distance between probability measures. In the second half, I discuss our recent work, on the use of efficient algorithms for approximating Wasserstein distance between two samples, to demonstrate directly stability of particle and ensemble Kalman filters as well as a relation to the RMSE.
Bio: Amit Apte is an applied mathematician with research interests in dynamical systems, data assimilation problems in earth sciences, and most recently, dynamics of the Indian summer monsoon. After his Ph.D in Physics at UTexas Austin and postdocs at SAMSI, Mathematics UNC Chapel Hill, and MSRI, Berkeley, he joined the Tata Institute of Fundamental Research in 2007 at the Centre for Applicable Mathematics (TIFR-CAM), moving to the International Centre for Theoretical Sciences (ICTS-TIFR) in 2013, before joining IISER-Pune in 2021 as the Chairperson of their newly started Department of Data Science.