(554b) Modeling Chaotic Spatiotemporal Dynamics with a Minimal Representation Using Neural ODEs
AIChE Annual Meeting
2021
2021 Annual Meeting
Engineering Sciences and Fundamentals
Turbulent, Reactive Flows and Flow Characterization
Wednesday, November 10, 2021 - 3:47pm to 4:04pm
In our approach, the change of coordinates is found by reducing the system dimension via an undercomplete autoencoder â a neural network (NN) that reduces then expands dimension. By varying the dimension of the reduced space, we find a minimal representation of the state. We then train a Neural ODE â a NN that approximates the right-hand side of an ODE â in the manifold coordinates. By learning an ODE, instead of the common approach of finding discrete time-maps, trajectories can be evolved arbitrarily far forward in time, and training data need not be evenly spaced in time. We test this method on a proxy for turbulence, the Kuramoto-Sivashinsky equation that has spatiotemporally chaotic dynamics, and find that accurate models can be generated for multiple domain sizes using data separated by 0.7 Lyapunov times. Finally, we apply this method to turbulent plane Couette flow.