Denoising and reconstruction of nonlinear dynamics using truncated reservoir computing

Area of Science:

• Computational Neuroscience
• Dynamical Systems Theory
• Signal Processing

Background:

• Distributed physical systems generate sparse, noisy measurements, necessitating advanced signal processing for system identification.
• Reconstructing unobserved dynamics is challenging due to the frequent unavailability of governing equations.
• Reservoir Computing (RC) offers efficient dynamical system simulation via random neural network connectivity.

Purpose of the Study:

• To develop and evaluate a novel Reservoir Computing (RC) method for noise filtering and reconstructing unobserved nonlinear dynamics.
• To explore RC's capability in distinguishing noise from deterministic system dynamics under various noise conditions.
• To introduce a new learning protocol with hyperparameter optimization for enhanced RC performance.

Main Methods:

• A novel Reservoir Computing (RC) framework was developed for noise filtering and nonlinear dynamics reconstruction.
• Hyperparameter optimization, including leakage rate and spectral radius, was employed.
• Network structure optimization through node and edge truncation was investigated.
• Performance was evaluated on the Lorenz attractor and adaptive exponential integrate-and-fire system.

Main Results:

• The proposed RC method effectively filters noise and reconstructs unobserved nonlinear dynamics.
• Denoising performance is enhanced by truncating redundant reservoir components and optimizing hyperparameters.
• The framework demonstrates good generalization to unseen, qualitatively different attractors.
• Competitive accuracy was achieved compared to the extended Kalman filter, especially at low signal-to-noise ratios and high frequencies.

Conclusions:

• The novel RC framework provides an effective solution for noise filtering and dynamics reconstruction in sparse, noisy data scenarios.
• Hyperparameter and network structure optimization are crucial for maximizing RC performance in challenging environments.
• The method shows promise for applications requiring robust system identification from limited and corrupted measurements.