Machine-learning parameter tracking with partial state observation
This addresses a key limitation in machine-learning methods for parameter tracking, which previously required full state observation, making it useful for applications like state estimation and control in complex systems.
The paper tackles the problem of tracking time-varying parameters in nonlinear dynamical systems from partial state observations, developing a model-free, data-driven framework using reservoir computing that accurately predicts parameter variations in real time.
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.