# Reservoir Computing with Diverse Timescales for Prediction of Multiscale Dynamics

arXiv: https://arxiv.org/abs/2108.09446 · HTML: https://mlsanity.com/paper/2108.09446/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 62 references that are in the map.
- First posted on arXiv 21 Aug 2021.

## Builds on (most cited first, 7 of 7)

- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model](https://mlsanity.com/paper/1803.04779/) (2018)
- [Exploiting Multiple Timescales in Hierarchical Echo State Networks](https://mlsanity.com/paper/2101.04223/) (2021)
- [Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy](https://mlsanity.com/paper/1707.00772/) (2017)
- [Performance boost of time-delay reservoir computing by non-resonant clock cycle](https://mlsanity.com/paper/1905.02534/) (2019)
- [Effective models and predictability of chaotic multiscale systems via machine learning](https://mlsanity.com/paper/2007.08634/) (2020)
- [Optimal responsiveness and collective oscillations emerging from the heterogeneity of inhibitory neurons](https://mlsanity.com/paper/2005.05596/) (2020)

## Built on by (most cited first, 13 of 13)

- [Learning noise-induced transitions by multi-scaling reservoir computing](https://mlsanity.com/paper/2309.05413/) (2023)
- [Effect of temporal resolution on the reproduction of chaotic dynamics via reservoir computing](https://mlsanity.com/paper/2302.10761/) (2023)
- [A Dynamic Systems Approach to Modelling Human-Machine Rhythm Interaction](https://mlsanity.com/paper/2407.09538/) (2024)
- [A novel Reservoir Architecture for Periodic Time Series Prediction](https://mlsanity.com/paper/2405.10102/) (2024)
- [Double projection for reconstructing dynamical systems: between stochastic and deterministic regimes](https://mlsanity.com/paper/2510.01089/) (2025)
- [Heterogeneous Reservoir Computing Models for Persian Speech Recognition](https://mlsanity.com/paper/2205.12594/) (2022)
- [Prediction Beyond the Medium Range with an Atmosphere-Ocean Model that Combines Physics-based Modeling and Machine Learning](https://mlsanity.com/paper/2405.19518/) (2024)
- [Predicting unobserved climate time series data at distant areas via spatial correlation using reservoir computing](https://mlsanity.com/paper/2406.03061/) (2024)
- [Prediction of Unobserved Bifurcation by Unsupervised Extraction of Slowly Time-Varying System Parameter Dynamics from Time Series Using Reservoir Computing](https://mlsanity.com/paper/2406.13995/) (2024)
- [Skewed Neuronal Heterogeneity Enhances Efficiency On Various Computing Systems](https://mlsanity.com/paper/2412.05126/) (2024)
- [Syntactic Learnability of Echo State Neural Language Models at Scale](https://mlsanity.com/paper/2503.01724/) (2025)
- [Reservoir Computing via Multi-Scale Random Fourier Features for Forecasting Fast-Slow Dynamical Systems](https://mlsanity.com/paper/2511.14775/) (2025)
- [Storage and selection of multiple chaotic attractors in minimal reservoir computers](https://mlsanity.com/paper/2603.15155/) (2026)

## Abstract (arXiv)

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of multiscale dynamics, we propose a reservoir computing (RC) model with diverse timescales by using a recurrent network of heterogeneous leaky integrator (LI) neurons. We evaluate computational performance of the proposed model in two time series prediction tasks related to four chaotic fast-slow dynamical systems. In a one-step-ahead prediction task where input data are provided only from the fast subsystem, we show that the proposed model yields better performance than the standard RC model with identical LI neurons. Our analysis reveals that the timescale required for producing each component of target multiscale dynamics is appropriately and flexibly selected from the reservoir dynamics by model training. In a long-term prediction task, we demonstrate that a closed-loop version of the proposed model can achieve longer-term predictions compared to the counterpart with identical LI neurons depending on the hyperparameter setting.