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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Toward data-driven reduced-order modeling and cont
rol of flows with complex chaotic dynamics - Micha
el Graham (University of Wisconsin-Madison)
DTSTART;TZID=Europe/London:20220606T160000
DTEND;TZID=Europe/London:20220606T170000
UID:TALK172943AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/172943
DESCRIPTION:Many fluid flows are characterized by chaotic dyna
mics\, a large number of degrees of freedom\, and
multiscale structure in space and time. We build o
n the idea that many dynamical systems that are no
minally described by a state variable of very high
or infinite dimension -- such as the Navier-Stoke
s equations governing fluid flow -- can be charact
erized with a much smaller number of dimensions\,
because the long-time dynamics lie on a finite-dim
ensional manifold. We describe a data-driven reduc
ed order modeling method that finds a coordinate r
epresentation of the manifold using an autoencoder
and then learns an ordinary differential equation
(ODE) describing the dynamics in these coordinate
s\, using the so-called neural ODE framework. With
the ODE representation\, data can be widely space
d. We apply this framework to spatiotemporal chaos
in the Kuramoto-Sivashinsky equation (KSE)\, chao
tic bursting dynamics of Kolmogorov flow\, and tra
nsitional turbulence in plane Couette flow\,
\;finding \;dramatic dimension reduction whil
e still yielding good predictions of short-time tr
ajectories and long-time statistics. For complex m
anifolds\, this approach can be combined with clus
tering to generate overlapping local representatio
ns that are particularly useful for intermittent d
ynamics. \;\nFinally\, we apply this framework
to a control problem that models drag reduction i
n turbulent flow. \; Deep reinforcement learn
ing (RL) control can discover control strategies f
or high-dimensional systems\, making it promising
for flow control. However\, a major challenge is t
hat substantial training data must be generated by
interacting with the target system\, making it co
stly when the flow system is computationally or ex
perimentally expensive. We mitigate this challenge
by obtaining a low-dimensional dynamical model fr
om a limited data set for the open-loop system\, t
hen learn an RL control policy using the model rat
her than the true system. We apply our method to d
ata from the KSE in a spatiotemporally chaotic reg
ime\, with aim of minimizing power consumption. Th
e learned policy is very effective at this aim\, &
nbsp\;achieving it by discovering and stabilizing
a low-dissipation steady state solution\, \;w
ithout having ever been given explicit information
about the existence of that solution. \;Give
n that near-wall turbulence is organized around si
mpler recurrent solutions\, the present approach m
ight be effective for drag reduction. \;
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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