论文标题
高斯流程Koopman模式分解
Gaussian Process Koopman Mode Decomposition
论文作者
论文摘要
在本文中，我们提出了基于无监督的高斯过程的Koopman模式分解的非线性概率生成模型。现有的Koopman模式分解的数据驱动方法重点是估计Koopman模式分解所指定的数量，即特征值，特征功能和模式。我们的模型可以同时估计这些数量和由未知动力学系统控制的潜在变量。此外，我们引入了一种有效的策略来通过低级别的协方差矩阵来估计模型的参数。将提出的模型应用于合成数据和现实世界流行病学数据集，我们表明使用估计参数可以进行各种分析。
In this paper, we propose a nonlinear probabilistic generative model of Koopman mode decomposition based on an unsupervised Gaussian process. Existing data-driven methods for Koopman mode decomposition have focused on estimating the quantities specified by Koopman mode decomposition, namely, eigenvalues, eigenfunctions, and modes. Our model enables the simultaneous estimation of these quantities and latent variables governed by an unknown dynamical system. Furthermore, we introduce an efficient strategy to estimate the parameters of our model by low-rank approximations of covariance matrices. Applying the proposed model to both synthetic data and a real-world epidemiological dataset, we show that various analyses are available using the estimated parameters.
