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Attractor learning for spatiotemporally chaotic dynamical systems using echo state networks with transfer learning
Mohammad Shah Alam, William Ott, Ilya Timofeyev
In this paper, we explore the predictive capabilities of echo state networks (ESNs) for the generalized Kuramoto-Sivashinsky (gKS) equation, an archetypal nonlinear PDE that exhibi…
Using Echo-State Networks to Reproduce Rare Events in Chaotic Systems
Anton Erofeev, Balasubramanya T. Nadiga, Ilya Timofeyev
We apply Echo-State Networks to predict time series and statistical properties of the competitive Lotka-Volterra model in the chaotic regime. In particular, we demonstrate that Ech…
Parametric Reduced Order Models for the Generalized Kuramoto--Sivashinsky Equations
Md Rezwan Bin Mizan, Maxim Olshanskii, Ilya Timofeyev
The paper studies parametric Reduced Order Models (ROMs) for the Kuramoto--Sivashinsky (KS) and generalized Kuramoto--Sivashinsky (gKS) equations. We consider several POD and POD-D…