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Updated: Oct 29, 2025

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Published on: September 11, 2019
Kernel-based parameter estimation of dynamical systems with unknown observation functions
Ofir Lindenbaum1, Amir Sagiv2, Gal Mishne3
1Program in Applied Mathematics, Yale University, 51 Prospect Street, New Haven, Connecticut 06511, USA.
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.
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