Tailored minimal reservoir computing: On the bidirectional connection between nonlinearities in the model and in data

Area of Science:

• Nonlinear dynamics
• Computational neuroscience
• Machine learning

Background:

• Reservoir computing (RC) models complex systems using nonlinear dynamics.
• Optimal RC design often requires matching model properties to data characteristics.
• The impact of nonlinearity degree on RC performance is not fully understood.

Purpose of the Study:

• To investigate how the degree of nonlinearity in input data influences optimal reservoir computer (RC) design.
• To determine the ideal alignment between a model's nonlinearity and the data's nonlinearity for enhanced predictive performance.
• To develop a method for estimating the minimal nonlinearity in unknown time series.

Main Methods:

• Reduced minimal RCs to a single tunable nonlinearity parameter.
• Utilized the generalized fractional Halvorsen system for controlled experiments.
• Swept model exponent to identify transitions in signal reconstruction and correlation dimension.
• Augmented classical RCs with fractional, generalized reservoir states.

Main Results:

• Prediction performance is maximized when the model's nonlinearity matches the data's nonlinearity.
• The smallest nonlinearity in the data must be matched for correct correlation dimension reconstruction.
• A practical method for estimating minimal nonlinearity in unknown time series was demonstrated.
• Augmenting RCs with fractional reservoir states improved performance, especially in resource-constrained settings.

Conclusions:

• Tailoring RC nonlinearity to data complexity is crucial for optimal performance.
• The proposed method offers a principled approach to estimating time series nonlinearity.
• Fractional reservoir states provide performance gains in classical RCs, particularly for physical systems.