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

TL;DR

This paper introduces a kernel-based method for estimating parameters of dynamical systems from a single high-dimensional observation, leveraging temporal dependencies in the data.

Contribution

It proposes a novel kernel-based score for parameter estimation that generalizes maximum likelihood to nonlinear systems with unknown observation functions.

Findings

Accurately estimates parameters of chaotic systems from limited data

Demonstrates effectiveness on double pendulum and Lorenz '63 models

Shows improved efficiency over existing methods

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.