Neural machine-based forecasting of chaotic dynamics

Chaotic dynamics is ubiquitous in nature. Traditionally, a good model representation of a certain system can help in predicting this system's future behavior. However, for a complex system, a physics-based model may not be easy to construct given the complexity of a system, in particular, those that exhibit chaotic behavior. Furthermore, due to the aperiodic nature of the motion and finite precision, a model-based prediction may only have relatively high accuracy over a short-time horizon, before significant growth of error occurs in the prediction. In this article, the authors explore an alternate modeling approach, which is based on data-driven modeling, to explore forecasting viability for systems that display chaotic dynamics. Specifically, a deep recurrent neural network architecture, a neural machine, is constructed for forecasting temporal evolution of different chaotic systems. Data obtained from simulations with well-known nonlinear dynamical system prototypes serve as training data for the chosen neural network. In practice, this simulation data may be replaced with field data. The trained system is studied to examine the forecasting ability. Two ordinary differential dynamical systems, namely the Lorenz'63 system and the Lorenz'96 system, and a partial differential system, the Kuramoto-Sivashinsky equation, are studied, and the numerical experiments conducted are presented here to demonstrate the forecasting viability of the constructed neural network.