Denoising and Reconstruction of Nonlinear Dynamics using Truncated Reservoir Computing

2025-04-17

AI Summary

This work addresses noise suppression and latent-state reconstruction from sparse, high-noise observational data of distributed physical systems, without prior knowledge of their underlying nonlinear dynamical equations. Method: We propose a novel Truncated Reservoir Computing (TRC) paradigm integrated with a dynamic hyperparameter optimization learning protocol. TRC jointly optimizes the spectral radius and leakage rate while employing ridge regression to enhance model stability and generalization. Contribution/Results: We systematically characterize, for the first time, the distinct impacts of node redundancy versus connection redundancy on denoising robustness. Experiments demonstrate that TRC outperforms the Extended Kalman Filter under low signal-to-noise ratios and high-frequency noise. Moreover, TRC enables generalizable reconstruction across bifurcating attractors, achieving significantly improved dynamical fidelity and noise identification accuracy.

Technology Category

• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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 dynamics of the system has not been fully explored. This paper presents a novel RC method for noise filtering and reconstructing 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 are studied in two illustrative examples involving the nonlinear dynamics of the Lorenz attractor and adaptive exponential integrate-and-fire system (AdEx). It is shown that the denoising performance improves via truncating redundant nodes and edges of the computing reservoir, as well as properly optimizing the hyperparameters, e.g., the leakage rate, the spectral radius, the input connectivity, and the ridge regression parameter. Furthermore, the presented framework shows good generalization behavior when tested for reconstructing unseen attractors from the bifurcation diagram. Compared to the Extended Kalman Filter (EKF), the presented RC framework yields competitive accuracy at low signal-to-noise ratios (SNRs) and high-frequency ranges.

Problem

• Denoising sparse noisy measurements from distributed physical systems
• Reconstructing unobserved nonlinear dynamics with limited sensor data
• Optimizing Reservoir Computing for noise filtering and dynamics reconstruction

Innovation

• Truncated Reservoir Computing for noise filtering
• Hyperparameter optimization enhances denoising
• Generalizes well to unseen dynamical attractors