Imperial College London
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ProfessorDanCrisan

Faculty of Natural Sciences, Department of Mathematics

Professor of Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8489d.crisan Website

 
 
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Location

 

670Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@unpublished{Cotter:2019,
author = {Cotter, C and Crisan, D and Holm, DD and Pan, W and Shevchenko, I},
publisher = {arXiv},
title = {A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equation},
url = {http://arxiv.org/abs/1907.11884v1},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - UNPB
AB  - In this work, we apply a particle filter with three additional procedures(model reduction, tempering and jittering) to a damped and forcedincompressible 2D Euler dynamics defined on a simply connected bounded domain.We show that using the combined algorithm, we are able to successfullyassimilate data from a reference system state (the ``truth") modelled by ahighly resolved numerical solution of the flow that has roughly $3.1\times10^6$degrees of freedom for $10$ eddy turnover times, using modest computationalhardware.  The model reduction is performed through the introduction of a stochasticadvection by Lie transport (SALT) model as the signal on a coarser resolution.The SALT approach was introduced as a general theory using a geometricmechanics framework from Holm, Proc. Roy. Soc. A (2015). This work follows onthe numerical implementation for SALT presented by Cotter et al, SIAMMultiscale Model. Sim. (2019) for the flow in consideration. The modelreduction is substantial: The reduced SALT model has $4.9\times 10^4$ degreesof freedom.  Forecast reliability and estimated asymptotic behaviour of the particlefilter are also presented.
AU  - Cotter,C
AU  - Crisan,D
AU  - Holm,DD
AU  - Pan,W
AU  - Shevchenko,I
PB  - arXiv
PY  - 2019///
TI  - A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equation
UR  - http://arxiv.org/abs/1907.11884v1
UR  - http://hdl.handle.net/10044/1/72321
ER  -
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