Machine-learning parameter tracking with partial state observation
Zheng-Meng Zhai Mohammadamin Moradi Bryan Glaz Mulugeta Haile Ying-Cheng Lai
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.