# Controlling nonlinear dynamical systems into arbitrary states using machine learning

arXiv: https://arxiv.org/abs/2102.12969 · HTML: https://mlsanity.com/paper/2102.12969/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 58 references that are in the map.
- First posted on arXiv 23 Feb 2021.

## Builds on (most cited first, 5 of 5)

- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers](https://mlsanity.com/paper/1910.00659/) (2019)
- [Theory of neuromorphic computing by waves: machine learning by rogue waves, dispersive shocks, and solitons](https://mlsanity.com/paper/1912.07044/) (2019)
- [Accuracy of neural networks for the simulation of chaotic dynamics: precision of training data vs precision of the algorithm](https://mlsanity.com/paper/2008.04222/) (2020)
- [Adding Filters to Improve Reservoir Computer Performance](https://mlsanity.com/paper/2008.10633/) (2020)

## Built on by (most cited first, 5 of 5)

- [Controlling Chaotic Maps using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2307.03813/) (2023)
- [Phase2vec: Dynamical systems embedding with a physics-informed convolutional network](https://mlsanity.com/paper/2212.03857/) (2022)
- [Controlling dynamical systems to complex target states using machine learning: next-generation vs. classical reservoir computing](https://mlsanity.com/paper/2307.07195/) (2023)
- [Digital twins of nonlinear dynamical systems](https://mlsanity.com/paper/2210.06144/) (2022)
- [Controlling Dynamical Systems into Unseen Target States Using Machine Learning](https://mlsanity.com/paper/2412.10251/) (2024)

## Abstract (arXiv)

We propose a novel and fully data driven control scheme which relies on machine learning (ML). Exploiting recently developed ML-based prediction capabilities of complex systems, we demonstrate that nonlinear systems can be forced to stay in arbitrary dynamical target states coming from any initial state. We outline our approach using the examples of the Lorenz and the R"ossler system and show how these systems can very accurately be brought not only to periodic but also to e.g. intermittent and different chaotic behavior. Having this highly flexible control scheme with little demands on the amount of required data on hand, we briefly discuss possible applications that range from engineering to medicine.