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

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