Dynamic system classifier

TL;DR

The paper introduces a Bayesian dynamic system classifier (DSC) that uses stochastic differential equations to characterize and classify complex oscillatory systems based on their time-dependent parameters, effective even with noisy data.

Contribution

It develops a novel Bayesian framework for classifying dynamical systems using stochastic differential equations with time-dependent parameters, focusing on oscillatory processes.

Findings

Classifiers perform well in low signal-to-noise conditions

The method effectively captures characteristic features of oscillatory systems

The approach provides a compact representation of system dynamics

Abstract

Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and classify complex dynamical systems is proposed within a Bayesian framework. To this end, we develop a dynamic system classifier (DSC). The DSC first abstracts training data of a system in terms of time dependent coefficients of the descriptive stochastic differential equation. Thereby the DSC identifies unique correlation structures within the training data. For definiteness we restrict the presentation of DSC to oscillation processes with a time dependent frequency {\omega}(t) and damping factor {\gamma}(t). Although real systems might be more complex, this simple oscillator captures many characteristic features. The {\omega} and {\gamma} timelines represent the abstract system characterization and permit the construction of efficient signal classifiers. Numerical experiments show that such classifiers perform well even in the low signal-to-noise regime.