# Machine-learning parameter tracking with partial state observation

arXiv: https://arxiv.org/abs/2311.09142 · HTML: https://mlsanity.com/paper/2311.09142/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 65 references that are in the map.
- First posted on arXiv 15 Nov 2023.

## Builds on (most cited first, 13 of 13)

- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (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)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)
- [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)
- [Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components](https://mlsanity.com/paper/2102.07819/) (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)
- [Model-free tracking control of complex dynamical trajectories with machine learning](https://mlsanity.com/paper/2309.11470/) (2023)
- [Sensor-based Gait Parameter Extraction with Deep Convolutional Neural Networks](https://mlsanity.com/paper/1609.03323/) (2016)

## Built on by (most cited first, 4 of 4)

- [Data-driven model discovery with Kolmogorov-Arnold networks](https://mlsanity.com/paper/2409.15167/) (2024)
- [Learning to learn ecosystems from limited data -- a meta-learning approach](https://mlsanity.com/paper/2410.07368/) (2024)
- [Reconstructing dynamics from sparse observations with no training on target system](https://mlsanity.com/paper/2410.21222/) (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)

## Abstract (arXiv)

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state observation of the underlying system and tacitly assume adiabatic changes in the parameter. Formulating an inverse problem and exploiting reservoir computing, we develop a model-free and fully data-driven framework to accurately track time-varying parameters from partial state observation in real time. In particular, with training data from a subset of the dynamical variables of the system for a small number of known parameter values, the framework is able to accurately predict the parameter variations in time. Low- and high-dimensional, Markovian and non-Markovian nonlinear dynamical systems are used to demonstrate the power of the machine-learning based parameter-tracking framework. Pertinent issues affecting the tracking performance are addressed.