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SUMMARY:Analysis of Ensemble Kalman Inversion - Claudia Schillings (Univer
 sity of Warwick)
DTSTART:20180112T113000Z
DTEND:20180112T123000Z
UID:TALK97534@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The Ensemble Kalman filter (EnKF) has had enormous impact on t
 he applied sciences since its introduction in the 1990s by Evensen and cow
 orkers. It is used for both data assimilation problems\, where the objecti
 ve is to estimate a partially observed time-evolving system\, and inverse 
 problems\, where the objective is to estimate a (typically distributed) pa
 rameter appearing in a differential equation.  In this talk we will focus 
 on the identification of parameters through observations of the response o
 f the system - the inverse problem. The EnKF can be adapted to this settin
 g by introducing artificial dynamics. Despite documented success as a solv
 er for such inverse problems\, there is very little analysis of the algori
 thm. In this talk\, we will discuss well-posedness and convergence results
  of the EnKF based on the continuous time scaling limits\, which allow to 
 derive estimates on the long-time behavior of the EnKF and\, hence\, provi
 de insights into the convergence properties of the algorithm. In particula
 r\, we are interested in the properties of the EnKF for a fixed ensemble s
 ize. Results from various numerical experiments supporting the theoretical
  findings will be presented.  This is joint work with Dirk Bloemker (U Aug
 sburg)\, Mike Christie (Heriot-Watt University)\, Andrew M. Stuart (Caltec
 h) and Philipp Wacker (FAU Erlangen-Nuernberg). 
LOCATION:Seminar Room 1\, Newton Institute
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