English

Deep learning to discover and predict dynamics on an inertial manifold

Machine Learning 2020-06-19 v3 Fluid Dynamics

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.

Keywords

Cite

@article{arxiv.2001.04263,
  title  = {Deep learning to discover and predict dynamics on an inertial manifold},
  author = {Alec J. Linot and Michael D. Graham},
  journal= {arXiv preprint arXiv:2001.04263},
  year   = {2020}
}

Comments

Accepted in Physical Review E

R2 v1 2026-06-23T13:09:41.983Z