# Digital twins of nonlinear dynamical systems: A perspective

arXiv: https://arxiv.org/abs/2309.11461 · HTML: https://mlsanity.com/paper/2309.11461/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 69 references that are in the map.
- First posted on arXiv 20 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Digital Twin: Values, Challenges and Enablers](https://mlsanity.com/paper/1910.01719/) (2019)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers](https://mlsanity.com/paper/1910.00659/) (2019)
- [Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius](https://mlsanity.com/paper/1910.04426/) (2019)
- [Anticipating synchronization with machine learning](https://mlsanity.com/paper/2103.13358/) (2021)
- [Machine-learning inference of fluid variables from data using reservoir computing](https://mlsanity.com/paper/1805.09917/) (2018)
- [Dynamical learning of dynamics](https://mlsanity.com/paper/1902.02875/) (2019)
- [Optimizing Memory in Reservoir Computers](https://mlsanity.com/paper/2201.01605/) (2022)
- [Reconstructing propagation networks with natural diversity and identifying hidden sources](https://mlsanity.com/paper/1407.4451/) (2014)

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

- [Data-driven model discovery with Kolmogorov-Arnold networks](https://mlsanity.com/paper/2409.15167/) (2024)

## Abstract (arXiv)

Digital twins have attracted a great deal of recent attention from a wide range of fields. A basic requirement for digital twins of nonlinear dynamical systems is the ability to generate the system evolution and predict potentially catastrophic emergent behaviors so as to providing early warnings. The digital twin can then be used for system "health" monitoring in real time and for predictive problem solving. In particular, if the digital twin forecasts a possible system collapse in the future due to parameter drifting as caused by environmental changes or perturbations, an optimal control strategy can be devised and executed as early intervention to prevent the collapse. Two approaches exist for constructing digital twins of nonlinear dynamical systems: sparse optimization and machine learning. The basics of these two approaches are described and their advantages and caveats are discussed.