Abstract
Minimal dimensional models are desirable for reduced computational costs in simulations as well as for applications such as model-based control. Long-time dynamics of flows often evolve on a low-dimensional manifold M in the full state space. We use neural networks to estimate M and the dynamics on it for two-dimensional Kolmogorov flow in a chaotic bursting regime. Outcomes include: a minimal dimension estimate, good short-time tracking and long-time statistics, as well as accurate predictions of bursting events.
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