Reservoir computing advances the ability to predict phase changes in chaotic systems

The ability to predict phase changes in chaotic systems is crucial for improving understanding of many physical or biological systems. A type of machine learning known as reservoir computing has shown potential for tracking complex spatiotemporal chaotic systems. Zhang et al. report an approach to reservoir computing for predicting the phase evolution of chaotic oscillators for a long time.

Using a chaotic food-web system and a classical chaotic oscillator as examples, the authors demonstrate that if the prediction criterion is relaxed to only the evolution of the phase variable, the prediction horizon can be orders of magnitude longer than predicting the evolution of the entire state variables.

“If one is happy with predicting the ups and downs of the chaotic oscillation instead of the evolution of the full dynamical state of the system, then the prediction time can be much longer,” said author Ying-Cheng Lai.

Although the prediction time using the method for full dynamical variables last only for five or six cycles, the authors argue it is useful for situations where phase information of the system is key, such as the ups and downs of a population in an ecological system or the polarity of a voltage variable in an electronic circuit.

“In a chaotic electronic circuit, one may be interested in the time evolution of a voltage variable but only in terms of its polarity. Complete information about the time evolution of the dynamical variables is not necessary – only the phase information is needed,” said Lai.

The researchers intend on expanding the method to test its ability for predicting the phase evolution for a network of oscillators instead of a single chaotic oscillator.

Source: “Predicting phase and sensing phase coherence in chaotic systems with machine learning,” by Chun Zhang, Junjie Jiang, Shi-Xian Qu, and Ying-Cheng Lai, Chaos (2020). The article can be accessed at https://doi.org/10.1063/5.0006304 .