Can neural networks predict dynamics they have never seen?
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Neural networks have proven to be remarkably successful for a wide range of complicated tasks, from image recognition and object detection to speech recognition and machine translation. One of their successes is the skill in prediction of future dynamics given a suitable training set of data. Previous studies have shown how Echo State Networks (ESNs), a subset of Recurrent Neural Networks, can successfully predict even chaotic systems for times longer than the Lyapunov time. This study shows that, remarkably, ESNs can successfully predict dynamical behavior that is qualitatively different from any behavior contained in the training set. Evidence is provided for a fluid dynamics problem where the flow can transition between laminar (ordered) and turbulent (disordered) regimes. Despite being trained on the turbulent regime only, ESNs are found to predict laminar behavior. Moreover, the statistics of turbulent-to-laminar and laminar-to-turbulent transitions are also predicted successfully, and the utility of ESNs in acting as an early-warning system for transition is discussed. These results are expected to be widely applicable to data-driven modelling of temporal behaviour in a range of physical, climate, biological, ecological and finance models characterized by the presence of tipping points and sudden transitions between several competing states.
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