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

Area of Science:

• Complex Systems
• Machine Learning
• Nonlinear Dynamics

Background:

• Machine learning (ML) prediction of chaotic dynamics is data-dependent.
• Numerical solutions of differential equations introduce scheme-dependent noise, hindering accurate chaotic system representation.
• Existing methods struggle with noise inherent in numerically generated chaotic time series.

Purpose of the Study:

• To propose a stochastic approach for generating training time series for chaotic dynamics.
• To characterize the predictability of chaotic systems using this stochastic method.
• To critically evaluate reservoir computing models for chaotic time series prediction.

Main Methods:

• Developed a stochastic approach to generate training time series for chaotic systems.
• Applied the method to analyze the Lorenz system and Anishchenko-Astakhov generator.
• Extended the approach to assess reservoir computing (RC) performance in surrogate modeling.

Main Results:

• The stochastic approach provides a more robust method for generating chaotic time series.
• Predictability characterization is improved by accounting for inherent system noise.
• Limitations of reservoir computing were identified in accurately modeling chaotic dynamics.

Conclusions:

• A stochastic time series generation method enhances machine learning for chaotic dynamics.
• This approach offers a more reliable way to assess predictability and model limitations.
• Reservoir computing shows limitations for surrogate modeling of complex chaotic systems.