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SUMMARY:The Filtering Distribution For Partially Observed Chaotic Dynamica
 l Systems - Stuart\, A (University of Warwick)
DTSTART:20140422T135500Z
DTEND:20140422T143000Z
UID:TALK52087@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-author: Daniel Sanz (University of Warwick)\n\nMany physica
 l systems can be successfully modelled by a deterministic dynamical system
  for which\, however\, the initial conditions may contain uncertainty. In 
 the presence of chaos this can lead to undesirable growth of uncertainty o
 ver time. However\, when noisy observations of the system are present thes
 e may be used to compensate for the uncertainty in the initial state. This
  scenario is naturally modelled by viewing the initial state as given by a
  probability distribution\, and to then condition this probability distrib
 ution on the noisy observations\, thereby reducing uncertainty. Filtering 
 refers to the situation where the conditional distribution on the system s
 tate is updated sequentially\, at the time of each observation. In this ta
 lk we investigate the asymptotic behaviour of this filtering distribution 
 for large time. We focus on a class of dissipative systems that includes t
 he Lorenz '63 and '96 models\, and the Navier-Stokes equations on a 2D tor
 us. We first st udy the behaviour of a variant on the 3DVAR filter\, creat
 ing a unified analysis which subsumes the existing work in [1\,2] which\, 
 itself\, builds on [3]. The optimality property of the true filtering dist
 ribution is then used\, when combined with this modified 3DVAR analysis\, 
 to provide general conditions on the observation of our wide class of chao
 tic dissipative systems which ensure that the filtering distributions conc
 entrate around the true state of the underlying system in the long-time as
 ymptotic regime.\n\n[1] C.E.A. Brett\, K.F. Lam\, K.J.H. Law\, D.S. McCorm
 ick\, M.R. Scott and A.M. Stuart\, ``Accuracy and stability of filters for
  dissipative PDEs.'' Physica D 245(2013).\n\n[2] K.J.H. Law\, A. Shukla an
 d A.M. Stuart\, ``Analysis of the 3DVAR Filter for the Partially Observed 
 Lorenz '63 Model.'' Discrete and Continuous Dynamical Systems A\, 34(2014)
 .\n\n[3] K. Hayden\, E. Olsen and E.S. Titi\, ``Discrete data assimilation
  in the Lorenz and 2D Navier-Stokes equations.'' Physica D 240(2011).\n
LOCATION:Seminar Room 1\, Newton Institute
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