Denoising and Reconstruction of Nonlinear Dynamics using Truncated Reservoir Computing
This work addresses noise filtering and dynamics reconstruction for distributed physical systems, offering a domain-specific incremental improvement over existing Reservoir Computing techniques.
The paper tackles the problem of denoising and reconstructing unobserved nonlinear dynamics from sparse, noisy sensor data, where governing equations are unknown, by introducing a novel Reservoir Computing method with hyperparameter optimization and node truncation. It demonstrates improved denoising performance in examples like the Lorenz attractor, showing competitive accuracy against the extended Kalman filter at low signal-to-noise ratios and high frequencies.
Measurements acquired from distributed physical systems are often sparse and noisy. Therefore, signal processing and system identification tools are required to mitigate noise effects and reconstruct unobserved dynamics from limited sensor data. However, this process is particularly challenging because the fundamental equations governing the dynamics are largely unavailable in practice. Reservoir Computing (RC) techniques have shown promise in efficiently simulating dynamical systems through an unstructured and efficient computation graph comprising a set of neurons with random connectivity. However, the potential of RC to operate in noisy regimes and distinguish noise from the primary smooth or non-smooth deterministic dynamics of the system has not been fully explored. This paper presents a novel RC method for noise filtering and reconstructing unobserved nonlinear dynamics, offering a novel learning protocol associated with hyperparameter optimization. The performance of the RC in terms of noise intensity, noise frequency content, and drastic shifts in dynamical parameters is studied in two illustrative examples involving the nonlinear dynamics of the Lorenz attractor and the adaptive exponential integrate-and-fire system. It is demonstrated that denoising performance improves by truncating redundant nodes and edges of the reservoir, as well as by properly optimizing hyperparameters, such as the leakage rate, spectral radius, input connectivity, and ridge regression parameter. Furthermore, the presented framework shows good generalization behavior when tested for reconstructing unseen and qualitatively different attractors. Compared to the extended Kalman filter, the presented RC framework yields competitive accuracy at low signal-to-noise ratios and high-frequency ranges.