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arXiv · 2001.04263

Deep learning to discover and predict dynamics on an inertial manifold

Alec J. Linot·Michael D. Graham
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Abstract

A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension reduction transforms between coordinates in the full state space and on the IM. Additional neural networks predict time-evolution on the IM. The formalism accounts for translation invariance and energy conservation, and substantially outperforms linear dimension reduction, reproducing very well key dynamic and statistical features of the attractor.

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BibTeXRIS

Alec J. Linot, Michael D. Graham. 2019-12-20. Deep learning to discover and predict dynamics on an inertial manifold. https://doi.org/10.1103/physreve.101.062209

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