论文标题
同步动力学中相互作用的操作者理论分析
Operator-theoretic Analysis of Mutual Interactions in Synchronized Dynamics
论文作者
论文摘要
分析同步非线性振荡器是非线性科学中最重要，最有吸引力的主题之一。通过了解振荡器之间的相互作用，我们可以找出同步过程。非线性科学中相互作用振荡器分析的一种有希望的方法是相模型的应用。在本文中，我们提出了一种基于相模型的数据驱动方法来提取同步振荡器的相互作用。最近，已经积极研究了将机器学习技术应用于物理学的估计模型。我们提出了一种运算符理论方法来估计相互作用振荡器的相模型。我们将估计问题减少到Koopman操作员的多参数特征值问题，这是描述动态系统的线性操作员。通过将问题减少到线性代数问题，我们可以从理论上表明所提出的方法相对于给定数据中的扰动是稳定的。
Analyzing synchronized nonlinear oscillators is one of the most important and attractive topics in nonlinear science. By understanding the interactions between the oscillators, we can figure out the synchronization process. A promising approach to the analysis of interacting oscillators in nonlinear science is the application of the phase model. In this paper, we propose a data-driven approach to extract mutual interactions of synchronized oscillators based on the phase model. Recently, applying machine learning techniques to estimate models in physics has been actively investigated. We propose an operator-theoretic approach to estimate the phase model of interacting oscillators. We reduce the estimation problem to a multiparameter eigenvalue problem of the Koopman operator, a linear operator that describes a dynamical system. By reducing the problem to a linear algebraic problem, we can theoretically show that the proposed approach is stable with respect to perturbations in the given data.
