# Denoising and Reconstruction of Nonlinear Dynamics using Truncated Reservoir Computing

arXiv: https://arxiv.org/abs/2504.13355 · HTML: https://mlsanity.com/paper/2504.13355/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 17 Apr 2025.

## Builds on (most cited first, 11 of 11)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Which Neural Net Architectures Give Rise To Exploding and Vanishing Gradients?](https://mlsanity.com/paper/1801.03744/) (2018)
- [Multifunctionality in a Reservoir Computer](https://mlsanity.com/paper/2008.06348/) (2020)
- [Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing](https://mlsanity.com/paper/2108.04074/) (2021)
- [Separation of Chaotic Signals by Reservoir Computing](https://mlsanity.com/paper/1910.10080/) (2019)
- [Controlling Chaos Using Edge Computing Hardware](https://mlsanity.com/paper/2406.12876/) (2024)
- [Role of non-linear data processing on speech recognition task in the framework of reservoir computing](https://mlsanity.com/paper/1906.02812/) (2019)
- [Reservoir Computing with Noise](https://mlsanity.com/paper/2303.00585/) (2023)
- [Fundamental aspects of noise in analog-hardware neural networks](https://mlsanity.com/paper/1907.09002/) (2019)
- [Creating New Chaotic Signals with Reservoir Computers](https://mlsanity.com/paper/2210.06250/) (2022)
- [Signal-noise separation using unsupervised reservoir computing](https://mlsanity.com/paper/2404.04870/) (2024)

## Built on by (most cited first, 1 of 1)

- [Robust and Efficient Communication in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2511.11393/) (2025)

## Abstract (arXiv)

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.