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CATEGORIES:BPI Seminar Series
SUMMARY:Searching for periodic orbits in turbulence with c
onvolutional neural networks - Dr Jacob Page (Univ
ersity of Cambridge)
DTSTART;TZID=Europe/London:20190509T113000
DTEND;TZID=Europe/London:20190509T123000
UID:TALK118465AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/118465
DESCRIPTION:Unstable periodic orbits (UPOs) are the building b
locks of chaotic attractors and possibly turbulent
attractors too. The current state-of-the-art for
finding UPOs in a turbulent flow begins with a sea
rch for `near recurrences' in a DNS time series\,
measured as local minima in an $l_2$-norm between
snapshots of the flow. The approach is crude and s
truggles to identify UPOs which are visited only f
leetingly or which may be spatially localised. In
this work we explore the use of convolutional neur
al networks (CNNs) as a means of performing a dime
nsionality reduction that respects the existence o
f UPOs and which can then be applied as a tool for
efficiently identifying these coherent structures
in turbulent data streams. We train a CNN in the
form of an autoencoder to reconstruct snapshots of
turbulent Kolmogorov flow (body-forced Navier Sto
kes equations on a 2-torus). The autoencoder reduc
es the dimensionality of the flow by orders of mag
nitude while its output is largely indistinguishab
le from the true turbulence. The network naturally
develops an embedding of the continuous translati
onal symmetry in the system\, and we exploit this
fact to define translation-independent observables
of encoded vorticity fields. These observables ca
n be used as a visualisation tool for comparing en
coded UPOs\, which cluster into distinct families
of coherent structures with different dynamic feat
ures. The suggestion that the network has learnt a
dimensionality reduction that is related to the e
xact coherent structures is confirmed by performin
g a recurrent flow analysis on encoded time series
using the translation-independent observable. The
approach results in the identification of an orde
r of magnitude more UPOs as compared to a standard
recurrent flow analysis over the same time interv
al. We will go on to assess the network's performa
nce at higher Reynolds numbers\, where only a hand
ful of exact coherent structures have been previou
sly identified.
LOCATION:Open Plan Area\, BP Institute\, Madingley Rise CB3
0EZ
CONTACT:Catherine Pearson
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