A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equation

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Title: A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equation
Authors: Cotter, C
Crisan, D
Holm, DD
Pan, W
Shevchenko, I
Item Type: Working Paper
Abstract: In this work, we apply a particle filter with three additional procedures (model reduction, tempering and jittering) to a damped and forced incompressible 2D Euler dynamics defined on a simply connected bounded domain. We show that using the combined algorithm, we are able to successfully assimilate data from a reference system state (the ``truth") modelled by a highly resolved numerical solution of the flow that has roughly $3.1\times10^6$ degrees of freedom for $10$ eddy turnover times, using modest computational hardware. The model reduction is performed through the introduction of a stochastic advection by Lie transport (SALT) model as the signal on a coarser resolution. The SALT approach was introduced as a general theory using a geometric mechanics framework from Holm, Proc. Roy. Soc. A (2015). This work follows on the numerical implementation for SALT presented by Cotter et al, SIAM Multiscale Model. Sim. (2019) for the flow in consideration. The model reduction is substantial: The reduced SALT model has $4.9\times 10^4$ degrees of freedom. Forecast reliability and estimated asymptotic behaviour of the particle filter are also presented.
Issue Date: 27-Jul-2019
URI: http://hdl.handle.net/10044/1/72321
Publisher: arXiv
Copyright Statement: © 2019 Author(s).
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering and Physical Sciences Research Council
Funder's Grant Number: EP/N023781/1
EP/N023781/1
Keywords: stat.AP
stat.AP
physics.flu-dyn
62P35, 76B99, 35Q31, 65C35
stat.AP
stat.AP
physics.flu-dyn
62P35, 76B99, 35Q31, 65C35
Notes: 44 pages, 16 figures
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Applied Mathematics and Mathematical Physics



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