Ensemble-based method for the Inverse Frobenius-Perron Operator Problem: Data Driven Global Analysis from Spatiotemporal "Movie" data
Tools
Tools
Tools
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]](http://epubs.surrey.ac.uk/style/images/fileicons/text.png) |
Text
ApproxMarkov_May.pdf - Accepted version Manuscript Restricted to Repository staff only until 2 June 2022. Download (1MB) |
Official URL: https://doi.org/10.1016/j.physd.2020.132603
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 : |
|
|||||||||
| 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 |
Downloads
Downloads per month over past year