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SUMMARY:Searching for periodic orbits in turbulence with convolutional neu
 ral networks - Dr Jacob Page (University of Cambridge)
DTSTART:20190509T103000Z
DTEND:20190509T113000Z
UID:TALK118465@talks.cam.ac.uk
CONTACT:Catherine Pearson
DESCRIPTION:Unstable periodic orbits (UPOs) are the building blocks of cha
 otic attractors and possibly turbulent attractors too. The current state-o
 f-the-art for finding UPOs in a turbulent flow begins with a search for `n
 ear 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 struggles
  to identify UPOs which are visited only fleetingly or which may be spatia
 lly localised. In this work we explore the use of convolutional neural net
 works (CNNs) as a means of performing a dimensionality reduction that resp
 ects the existence of UPOs and which can then be applied as a tool for eff
 iciently identifying these coherent structures in turbulent data streams. 
 We train a CNN in the form of an autoencoder to reconstruct snapshots of t
 urbulent Kolmogorov flow (body-forced Navier Stokes equations on a 2-torus
 ). The autoencoder reduces the dimensionality of the flow by orders of mag
 nitude while its output is largely indistinguishable from the true turbule
 nce. The network naturally develops an embedding of the continuous transla
 tional symmetry in the system\, and we exploit this fact to define transla
 tion-independent observables of encoded vorticity fields. These observable
 s can be used as a visualisation tool for comparing encoded UPOs\, which c
 luster into distinct families of coherent structures with different dynami
 c features. The suggestion that the network has learnt a dimensionality re
 duction that is related to the exact coherent structures is confirmed by p
 erforming a recurrent flow analysis on encoded time series using the trans
 lation-independent observable. The approach results in the identification 
 of an order of magnitude more UPOs as compared to a standard recurrent flo
 w analysis over the same time interval. We will go on to assess the networ
 k's performance at higher Reynolds numbers\, where only a handful of exact
  coherent structures have been previously identified.
LOCATION:Open Plan Area\, BP Institute\, Madingley Rise CB3 0EZ
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