Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session ZC33: NLD Bifurcations and Chaos
12:50 PM–2:21 PM,
Tuesday, November 21, 2023
Room: 159AB
Chair: George Papadakis, Imperial College London
Abstract: ZC33.00004 : Learning Chaotic Dynamics through DMD and Neural Networks*
1:29 PM–1:42 PM
Presenter:
Daniel J Alford-Lago
(San Diego State University)
Authors:
Christopher W Curtis
(San Diego State University)
Daniel J Alford-Lago
(San Diego State University)
Erik Bollt
(Clarkson University)
Andrew Tuma
(San Diego State University)
We present extensions to DMD using autoencoders coupled with Takens embeddings that allow us to accurately learn and then predict dynamics across a range of chaotic dynamical systems. These include the classic Lorenz-63 system, the multiscale Rossler system, and the Kuramoto-Sivashinsky equations. The success of our approach rests on allowing the autoencoders to embed dynamics in higher dimensional spaces while also making the Takens embeddings adaptive during the training of the autoencoders. Together, we obtain high reconstruction accuracies over test data while also allowing for nontrivial predictive windows. Likewise, we also explore the impact of our autoencoder networks by studying how they change the mutual information shared across different dimensions in the dynamics. Experiments show that the encoding process significantly alters the information between dimensions, helping to explain better the role neural networks play in learning dynamical systems.
*This work was supported in part by ONR grant N00014-23-1-2106, the Naval Information Warfare Center, and ARO grant W911NF-16-1-0081.
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