Kernel-based parameter estimation of dynamical systems with unknown observation functions

Ofir Lindenbaum, Amir Sagiv, Gal Mishne, Ronen Talmon

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal, for example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the underlying system's parameters by measuring its time-evolution only once? The key information for performing this estimation lies in the temporal inter-dependencies between the signal and the model. We propose a kernel-based score to compare these dependencies. Our score generalizes a maximum likelihood estimator for a linear model to a general nonlinear setting in an unknown feature space. We estimate the system's underlying parameters by maximizing the proposed score. We demonstrate the accuracy and efficiency of the method using two chaotic dynamical systems - the double pendulum and the Lorenz '63 model.

Original languageEnglish
Article number043118
JournalChaos
Volume31
Issue number4
DOIs
StatePublished - 1 Apr 2021
Externally publishedYes

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© 2021 Author(s).

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