Many fluid flows are characterised by chaotic dynamics, a large number of degrees of freedom, and multiscale structure in space and time.
Michael’s research builds on the idea that many dynamical systems that are nominally described by a state variable of very high or infinite dimension, such as the Navier-Stokes equations governing fluid flow, can be characterised with a much smaller number of dimensions, because the long-time dynamics lie on a finite-dimensional manifold. We describe a data-driven reduced order modelling method that finds a coordinate representation of the manifold using an autoencoder and then learns an ordinary differential equation (ODE) describing the dynamics in these coordinates, using the so-called neural ODE framework. With the ODE representation, data can be widely spaced.
Michael’s work applies this framework to spatiotemporal chaos in the Kuramoto-Sivashinsky equation (KSE), chaotic bursting dynamics of Kolmogorov flow, and transitional turbulence in plane Couette flow, finding dramatic dimension reduction while still yielding good predictions of short-time trajectories and long-time statistics. For complex manifolds, this approach can be combined with clustering to generate overlapping local representations that are particularly useful for intermittent dynamics.
Finally, the team apply this framework to a control problem that models drag reduction in turbulent flow. Deep reinforcement learning (RL) control can discover control strategies for high-dimensional systems, making it promising for flow control. However, a major challenge is that substantial training data must be generated by interacting with the target system, making it costly when the flow system is computationally or experimentally expensive.
The team mitigate this challenge by obtaining a low-dimensional dynamical 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. They apply the method to data from the KSE in a spatiotemporally chaotic regime, with aim of minimising power consumption. The learned policy is very effective at this aim, achieving it by discovering and stabilising a low-dissipation steady state solution, without having ever been given explicit information about the existence of that solution. Given that near-wall turbulence is organised around simpler recurrent solutions, the present approach might be effective for drag reduction.
About the Aerodynamics & Control Seminar Series
The Aerodynamics & Control Seminars, hosted by the Department of Aeronautics, are a series of talks by internationally renowned academics covering a broad range of topics in fluid mechanics, control, and the intersection of these two areas.