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The applicability of machine learning for predicting chaotic dynamics reliesheavily upon the data used in the training stage. Chaotic time series obtainedby numerically solving ordinary differential equations embed a complicatednoise of the applied numerical scheme. Such a dependence of the solution on thenumeric scheme leads to an inadequate representation of the real chaoticsystem. A stochastic approach for generating training times series andcharacterising their predictability is suggested to address this problem. Theapproach is applied for analysing two chaotic systems with known properties,Lorenz system and Anishchenko-Astakhov generator. Additionally, the approach isextended to critically assess a reservoir computing model used for chaotic timeseries prediction. Limitations of reservoir computing for surrogate modellingof chaotic systems are highlighted.

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