Machine-learning parameter tracking with partial state observation

Aug 3, 2026

Complex, nonlinear dynamical systems often contain time-varying parameters whose accurate tracking is essential for state estimation, prediction, and control. Existing machine-learning approaches typically assume full state observation and adiabatic parameter changes. This work formulates an inverse-problem strategy using reservoir computing to build a model-free, fully data-driven framework for real-time tracking of time-varying parameters from partial state observation. Training uses time-series data from a subset of variables at a small number of known parameter values, enabling accurate future parameter variation prediction. Markovian and non-Markovian nonlinear systems of different dimensions are used to demonstrate performance while addressing key factors affecting tracking.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages6

Reading Time15 min

AccessFree to download

Introduction

Motivation for time-varying parameter tracking

Inverse problem formulation and partial observation

Machine-learning framework

Limits of existing methods

Proposed reservoir computing approach

Setup and learning scheme

arXiv :2311 .09142v1 [ cs .LG] 15 Nov 2023 Machine-learning parameter tracking with partial state observation Zheng-Meng Zhai, 1 Mohammadamin Moradi, 1 Bryan Glaz,2 Mulugeta Haile,3 and Ying-Cheng Lai 1, 4, ∗ 1 School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA 2 Army Research Directorate, DEVCOM Army Research Laboratory, 2800 Powder Mill Road, Adelphi, MD 20783-1138, USA 3 Army Research Directorate, DEVCOM Army Research Laboratory, 6340 Rodman Road, Aberdeen Proving Ground, MD 21005-5069, USA 4 Department of Physics, Arizona State University, Tempe, Arizona 85287, USA (Dated: November 16, 2023) 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. The behavior of a nonlinear dynamical system is controlled by its parameters. In a real-world environment, the parameters typically change or drift with time. For example, when an optical sensor system is deployed to an outdoor environment, climatic disturbances such as temperature and humidity fluctuations can cause the geometrical and material parameters of the system to change with time. In an ecological system, seasonal fluctuations and human influences on the environment can induce changes in the parameters underlying the population dynamics such as the carrying capacity and species decay rates. Often, due to the complex interactions between the system and the environment, the simplistic assumption that the parameters drift linearly with time is not valid. Rather, the variations of the parameters with time can be complicated. A generic feature of nonlinear dynamical systems is that even a small parameter change can lead to characteristically different and even catastrophic behaviors. For example, a nonlinear system can typically exhibit a variety of bifurcations including a crisis [1] at which a chaotic attractor is destroyed and replaced by transient chaos [2], leading to system collapse. Being able to predict or forecast how some key system parameters change with time into the future can lead to control strategies to prevent system collapse. The problem of tracking parameter variations is an inverse problem, which is difficult even if an accurate mathematical model of the system is known. Our assumption is that the parameter of interest cannot be directly accessed or measured, so tracking its variations will need to be done indirectly using the measurements of some accessible dynamical variables of the system. Suppose that a key parameter will change with time in the future but, at present the system is stationary so that a few distinct values of this parameter can be measured, together with the time series of a subset of the dynamical variables. A scenario is that an instrument or device is to be deployed in certain missions where the harsh and nonstationary environment will cause the key parameter to change with time. Before deployment, the device can be tested in a controlled laboratory environment where the values of the parameter and the corresponding time series c

FAQs

Why is tracking time-varying parameters important in nonlinear dynamical systems?

Because parameters control system behavior, and real-world environments often cause them to drift over time, affecting estimation, prediction, and control and potentially leading to complex or catastrophic dynamics.

What key assumptions does the proposed framework make?

The target parameter cannot be directly measured; instead, tracking is performed indirectly from measurements of a partial subset of dynamical variables, using training data from only a small number of known parameter values.

How does reservoir computing enable parameter tracking from partial observations?

The method uses reservoir computing as the learning architecture and constructs integrated input time-series vectors from segmented measurements, mapping them to the parameter output so time variations can be predicted in real time.

Aug 3, 2026

Uploaded by Ava Thompson