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SUMMARY:Filtering partially observed chaotic deterministic dynamical syste
 ms - Sanz-Alonso\, D (University of Warwick)
DTSTART:20140317T151500Z
DTEND:20140317T155500Z
UID:TALK51460@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Many physical systems can be successfully modelled by a determ
 inistic dynamical system for which\, however\, the initial conditions may 
 contain uncertainty. In the presence of chaos this can lead to undesirable
  growth of uncertainty over time. However\, when noisy observations of the
  system are present these may be used to compensate for the uncertainty in
  the initial state. This scenario is naturally modelled by viewing the ini
 tial state as given by a probability distribution\, and to then condition 
 this probability distribution on the noisy observations\, thereby reducing
  uncertainty. Filtering refers to the situation where the conditional dist
 ribution on the system state is updated sequentially\, at the time of each
  observation. In this talk we investigate the asymptotic behaviour of this
  filtering distribution for large time.\n \nWe focus on a class of dissipa
 tive systems that includes the Lorenz '63 and '96 models\, and the Navier-
 Stokes equations on a 2D torus. We first study the behaviour of a variant 
 on the 3DVAR filter\, creating a unified analysis which subsumes the exist
 ing work in [1\,2] which\, itself\, builds on [3]. The optimality property
  of the true filtering distribution is then used\, when combined with this
  modified 3DVAR analysis\, to provide general conditions on the observatio
 n of our wide class of chaotic dissipative systems which ensure that the f
 iltering distributions concentrate around the true state of the underlying
  system in the long-time asymptotic regime.\n \n[1] C.E.A. Brett\, K.F. La
 m\, K.J.H. Law\, D.S. McCormick\, M.R. Scott and A.M. Stuart\, ``Accuracy 
 and stability of filters for dissipative PDEs.'' Physica D 245(2013). [2] 
 K.J.H. Law\, A. Shukla and A.M. Stuart\, ``Analysis of the 3DVAR Filter fo
 r the Partially Observed Lorenz '63 Model.'' Discrete and Continuous Dynam
 ical Systems A\, 34(2014). [3] K. Hayden\, E. Olsen and E.S. Titi\, ``Disc
 rete data assimilation in the Lorenz and 2D Navier-Stokes equations.'' Phy
 sica D 240(2011).\n
LOCATION:Seminar Room 1\, Newton Institute
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