论文标题
熵转移操作员
Entropic transfer operators
论文作者
论文摘要
我们提出了一个新概念，用于在动态系统中转移和库普曼运营商的正则化和离散化。我们的方法基于两种概率度量之间的熵正则最佳运输。特别是，我们使用最佳运输计划来构建某些转移或Koopman运算符的有限维近似，该近似可以通过计算进行分析。我们证明，离散操作员的频谱收敛于一个正规化的原始操作员，对离散的离散和原始外围光谱之间的关系进行了详细分析，用于$ n $ torus上的旋转图，并为三个数值实验提供代码，包括基于一个基于smill smill tragemate confucort的轨迹数据，以恢复过弹性数据，从而恢复了该型号的概述。
We propose a new concept for the regularization and discretization of transfer and Koopman operators in dynamical systems. Our approach is based on the entropically regularized optimal transport between two probability measures. In particular, we use optimal transport plans in order to construct a finite-dimensional approximation of some transfer or Koopman operator which can be analysed computationally. We prove that the spectrum of the discretized operator converges to the one of the regularized original operator, give a detailed analysis of the relation between the discretized and the original peripheral spectrum for a rotation map on the $n$-torus and provide code for three numerical experiments, including one based on the raw trajectory data of a small biomolecule from which its dominant conformations are recovered.
