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A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equation
File | Description | Size | Format | |
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1907.11884v1.pdf | Working paper | 10.01 MB | Adobe PDF | View/Open |
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 Applied Mathematics and Mathematical Physics Mathematics |