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SUMMARY:Toward data-driven reduced-order modeling and control of flows wit
 h complex chaotic dynamics - Michael Graham (University of Wisconsin-Madis
 on)
DTSTART:20220606T150000Z
DTEND:20220606T160000Z
UID:TALK172943@talks.cam.ac.uk
DESCRIPTION:Many fluid flows are characterized by chaotic dynamics\, a lar
 ge number of degrees of freedom\, and multiscale structure in space and ti
 me. We build on the idea that many dynamical systems that are nominally de
 scribed by a state variable of very high or infinite dimension -- such as 
 the Navier-Stokes equations governing fluid flow -- can be characterized w
 ith a much smaller number of dimensions\, because the long-time dynamics l
 ie on a finite-dimensional manifold. We describe a data-driven reduced ord
 er modeling method that finds a coordinate representation of the manifold 
 using an autoencoder and then learns an ordinary differential equation (OD
 E) describing the dynamics in these coordinates\, using the so-called neur
 al ODE framework. With the ODE representation\, data can be widely spaced.
  We apply this framework to spatiotemporal chaos in the Kuramoto-Sivashins
 ky equation (KSE)\, chaotic bursting dynamics of Kolmogorov flow\, and tra
 nsitional turbulence in plane Couette flow\, &nbsp\;finding &nbsp\;dramati
 c dimension reduction while still yielding good predictions of short-time 
 trajectories and long-time statistics. For complex manifolds\, this approa
 ch can be combined with clustering to generate overlapping local represent
 ations that are particularly useful for intermittent dynamics.&nbsp\;\nFin
 ally\, we apply this framework to a control problem that models drag reduc
 tion in turbulent flow. &nbsp\; Deep reinforcement learning (RL) control c
 an discover control strategies for high-dimensional systems\, making it pr
 omising for flow control. However\, a major challenge is that substantial 
 training data must be generated by interacting with the target system\, ma
 king it costly when the flow system is computationally or experimentally e
 xpensive. We mitigate this challenge by obtaining a low-dimensional dynami
 cal model from a limited data set for the open-loop system\, then learn an
  RL control policy using the model rather than the true system. We apply o
 ur method to data from the KSE in a spatiotemporally chaotic regime\, with
  aim of minimizing power consumption. The learned policy is very effective
  at this aim\, &nbsp\;achieving it by discovering and stabilizing a low-di
 ssipation steady state solution\, &nbsp\;without having ever been given ex
 plicit information about the existence of that solution. &nbsp\;Given that
  near-wall turbulence is organized around simpler recurrent solutions\, th
 e present approach might be effective for drag reduction. &nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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