University of Surrey

Test tubes in the lab Research in the ATI Dance Research

Ensemble-based method for the Inverse Frobenius-Perron Operator Problem: Data Driven Global Analysis from Spatiotemporal "Movie" data

Santitissadeekorn, Naratip and Bollt, Erik M. (2020) Ensemble-based method for the Inverse Frobenius-Perron Operator Problem: Data Driven Global Analysis from Spatiotemporal "Movie" data Physica D: Nonlinear Phenomena, 411, 132603.

[img] Text
ApproxMarkov_May.pdf - Accepted version Manuscript
Restricted to Repository staff only until 2 June 2022.

Download (1MB)

Abstract

Given a sequence of empirical distribution data (e.g. a movie of a spatiotemporal process such as a fluid flow), this work develops an ensemble data assimilation method to estimate the transition probability that represents a finite approximation of the Frobenius-Perron operator. This allows a dynamical systems knowledge to be incorporated into a prior ensemble, which provides sensible estimates in instances of limited observation. We demonstrate improved estimates over a constrained optimization approach (based on a quadratic programming problem) which does not impose a prior on the solution except for Markov properties. The estimated transition probability then enables several probabilistic analysis of dynamical systems. We focus only on the identification of coherent patterns from the estimated Markov transition to demonstrate its application as a proof-of-concept. To the best of our knowledge, there have not been many works on data-driven methods to identify coherent patterns from this type of data. While here the results are presented only in the context of dynamical systems applications, this work we present here has the potential to make a contribution in wider application areas that require the estimation of transition probabilities from a time-ordered spatio-temporal distribution data.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Santitissadeekorn, Naratipn.santitissadeekorn@surrey.ac.uk
Bollt, Erik M.
Date : 3 June 2020
DOI : 10.1016/j.physd.2020.132603
Copyright Disclaimer : © 2020 Elsevier B.V. All rights reserved.
Depositing User : James Marshall
Date Deposited : 10 Jun 2020 09:58
Last Modified : 10 Jun 2020 10:54
URI: http://epubs.surrey.ac.uk/id/eprint/857317

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year


Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800