# Controlling dynamical systems to complex target states using machine learning: next-generation vs. classical reservoir computing

arXiv: https://arxiv.org/abs/2307.07195 · HTML: https://mlsanity.com/paper/2307.07195/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 14 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2203.13294/) (2022)
- [Controlling nonlinear dynamical systems into arbitrary states using machine learning](https://mlsanity.com/paper/2102.12969/) (2021)
- [Time Shifts to Reduce the Size of Reservoir Computers](https://mlsanity.com/paper/2205.02267/) (2022)
- [Breaking Symmetries of the Reservoir Equations in Echo State Networks](https://mlsanity.com/paper/2010.07103/) (2020)

## Built on by (most cited first, 3 of 3)

- [Extrapolating tipping points and simulating non-stationary dynamics of complex systems using efficient machine learning](https://mlsanity.com/paper/2312.06283/) (2023)
- [Controlling Dynamical Systems into Unseen Target States Using Machine Learning](https://mlsanity.com/paper/2412.10251/) (2024)
- [Inference of Unknown Dynamical Components Using Next Generation Reservoir Computing: From Chaotic Systems to Climate Data](https://mlsanity.com/paper/2609.24754/) (2026)

## Abstract (arXiv)

Controlling nonlinear dynamical systems using machine learning allows to not only drive systems into simple behavior like periodicity but also to more complex arbitrary dynamics. For this, it is crucial that a machine learning system can be trained to reproduce the target dynamics sufficiently well. On the example of forcing a chaotic parametrization of the Lorenz system into intermittent dynamics, we show first that classical reservoir computing excels at this task. In a next step, we compare those results based on different amounts of training data to an alternative setup, where next-generation reservoir computing is used instead. It turns out that while delivering comparable performance for usual amounts of training data, next-generation RC significantly outperforms in situations where only very limited data is available. This opens even further practical control applications in real world problems where data is restricted.