论文标题
使用Wasserstein Metric的Perron-Frobenius操作员的数据驱动近似
Data-Driven Approximation of the Perron-Frobenius Operator Using the Wasserstein Metric
论文作者
论文摘要
该手稿引入了一个回归型公式，用于通过依靠数据的分布快照来近似perron-frobenius操作员。这些快照可能代表颗粒的密度。 Wasserstein指标被杠杆化以在分布空间中定义合适的功能优化。该公式允许寻求合适的动力学，以插入功能空间中的分布流。得出和使用的一阶必要条件被得出并用于构建近似算法的梯度流量。该框架用数值模拟为例。
This manuscript introduces a regression-type formulation for approximating the Perron-Frobenius Operator by relying on distributional snapshots of data. These snapshots may represent densities of particles. The Wasserstein metric is leveraged to define a suitable functional optimization in the space of distributions. The formulation allows seeking suitable dynamics so as to interpolate the distributional flow in function space. A first-order necessary condition for optimality is derived and utilized to construct a gradient flow approximating algorithm. The framework is exemplied with numerical simulations.
