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Neural networks have proven to be remarkably successful for a wide range ofcomplicated tasks, from image recognition and object detection to speechrecognition and machine translation. One of their successes is the skill inprediction of future dynamics given a suitable training set of data. Previousstudies have shown how Echo State Networks (ESNs), a subset of Recurrent NeuralNetworks, can successfully predict even chaotic systems for times longer thanthe Lyapunov time. This study shows that, remarkably, ESNs can successfullypredict dynamical behavior that is qualitatively different from any behaviorcontained in the training set. Evidence is provided for a fluid dynamicsproblem where the flow can transition between laminar (ordered) and turbulent(disordered) regimes. Despite being trained on the turbulent regime only, ESNsare found to predict laminar behavior. Moreover, the statistics ofturbulent-to-laminar and laminar-to-turbulent transitions are also predictedsuccessfully, and the utility of ESNs in acting as an early-warning system fortransition is discussed. These results are expected to be widely applicable todata-driven modelling of temporal behaviour in a range of physical, climate,biological, ecological and finance models characterized by the presence oftipping points and sudden transitions between several competing states.

Can neural networks predict dynamics they have never seen?