A recurrent neural network framework with an adaptive training strategy for long-time predictive modeling of nonlinear dynamical systems

Long-time prediction of future states has been challenging in data-driven modeling of nonlinear dynamical systems as the prediction error accumulates over the prediction horizon. One of the potential reasons is the lack of robustness for the data-driven model. In this study we present a recurrent neural network (RNN) framework with an adaptive training strategy to model nonlinear dynamical systems from data for long-time prediction of future states. Specifically, we exploit the recurrence of network to improve the model robustness by explicitly incorporating the multi-step prediction with error accumulation into model training. Furthermore, we introduce an adaptive training strategy, where the prediction horizon gradually increases from a small value to facilitate the RNN training. We demonstrate the proposed approach on a family of Duffing oscillators, including autonomous and non-autonomous systems with various attractors, and discuss its advantages and limitations.