Kernel-based parameter estimation of dynamical systems with unknown observation functions
This work addresses parameter estimation for dynamical systems in experimental settings where observation functions are unknown, offering a novel approach but with incremental advancements in kernel methods.
The authors tackled the problem of estimating parameters in low-dimensional dynamical systems from high-dimensional observations with unknown observation functions, proposing a kernel-based score that generalizes maximum likelihood estimation to nonlinear settings. They demonstrated the method's accuracy and efficiency on chaotic systems like the double pendulum and Lorenz '63 model, achieving concrete improvements in parameter estimation.
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.