Stochastic approach for assessing the predictability of chaotic time series using reservoir computing

The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of the applied numerical scheme. Such a dependence of the solution on the numeric scheme leads to an inadequate representation of the real chaotic system. A stochastic approach for generating training time series and characterizing their predictability is suggested to address this problem. The approach is applied for analyzing two chaotic systems with known properties, the Lorenz system and the Anishchenko-Astakhov generator. Additionally, the approach is extended to critically assess a reservoir computing model used for chaotic time series prediction. Limitations of reservoir computing for surrogate modeling of chaotic systems are highlighted.