Title:
Data-driven estimation of inertial manifold dimension for chaotic Kolmogorov flow and time evolution on the manifold
Part 3: Data-driven dimension reduction, dynamic modeling, and control of complex chaotic systems
Data-driven estimation of inertial manifold dimension for chaotic Kolmogorov flow and time evolution on the manifold
Part 3: Data-driven dimension reduction, dynamic modeling, and control of complex chaotic systems
Author(s)
Pérez De Jesús, Carlos
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Abstract
Model reduction techniques have previously been applied to evolve the Navier-Stokes equations in time, however finding the minimal dimension needed to correctly capture the key dynamics is not a trivial task. To estimate this dimension we trained an undercomplete autoencoder on weakly chaotic vorticity data (32x32 grid) from Kolmogorov flow simulations, tracking the reconstruction error as a function of dimension. We also trained a discrete time stepper that evolves the reduced order model with a nonlinear dense neural network. The trajectory travels in the vicinity of relative periodic orbits (RPOs) followed by sporadic bursting events. At a dimension of five (as opposed to the full state dimension of 1024), power input-dissipation probability density function is well-approximated; Fourier coefficient evolution shows that the trajectory correctly captures the heteroclinic connections (bursts) between the different RPOs, and the prediction and true data track each other for approximately a Lyapunov time.
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Date Issued
2021-11-03
Extent
57:49 minutes
Resource Type
Moving Image
Resource Subtype
Lecture