论文标题
基于内核的参数估计具有未知观察功能的动力学系统
Kernel-based parameter estimation of dynamical systems with unknown observation functions
论文作者
论文摘要
在实验中观察到低维动力系统作为高维信号。例如，一个混乱的摆系统的视频。假设我们知道到一些未知参数的动力学模型，我们可以通过仅测量其时间进化一次来估计基础系统的参数吗？执行此估计的关键信息在于信号与模型之间的时间相互依赖性。我们提出一个基于内核的分数来比较这些依赖性。我们的分数将线性模型的最大似然估计器推广到未知特征空间中的一般非线性设置。我们通过最大化提出的分数来估计系统的基础参数。我们使用两个混乱的动力学系统（双摆和Lorenz '63模型）证明了该方法的准确性和效率。
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.
