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.
翻译：低维动态系统作为高维信号在实验中观察到; 例如, 一个混乱的钟表系统的视频。 假设我们知道一些未知参数的动态模型, 我们能否通过只测量一次其时间演变来估计基本系统参数? 进行这一估计的关键信息在于信号和模型之间的时间相互依存关系。 我们提出一个以内核为基础的分数来比较这些依赖关系。 我们的分数将线性模型的最大可能性估计器与未知特征空间的一般非线性设置相容。 我们通过尽量扩大提议的分数来估计系统的基本参数。 我们用两种混乱的动态系统—— 双钟和Lorenz'63 模型—— 来显示方法的准确性和有效性。
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