Attractor learning for spatiotemporally chaotic dynamical systems using echo state networks with transfer learning

In this paper, we explore the predictive capabilities of echo state networks (ESNs) for the generalized Kuramoto–Sivashinsky (gKS) equation, an archetypal nonlinear partial differential equation (PDE) that exhibits spatiotemporal chaos. Our research focuses on predicting changes in long-term statistical patterns of the gKS model that result from varying the dispersion relation or the length of the spatial domain. We use transfer learning to adapt ESNs to different parameter settings and successfully capture changes in the underlying chaotic attractor. Previous work has shown that transfer learning can be used effectively with ESNs for a single-orbit prediction. The novelty of our paper lies in our use of this pairing to predict the long-term statistical properties of spatiotemporally chaotic PDEs. Nevertheless, we also show that transfer learning nontrivially improves the length of time that predictions of individual gKS trajectories remain accurate.