Perron-Frobenius算子的数据驱动Wasserstein度量逼近
Data-Driven Approximation of the Perron-Frobenius Operator Using the Wasserstein Metric
摘要：
这篇手稿介绍了一个回归型配方近似的Perron-Frobenius算子依赖于分布快照的数据。这些快照可以表示粒子的密度。利用Wasserstein度量在分布空间中定义合适的函数优化。该公式允许寻找合适的动力学，以便在函数空间内插分配流。导出了最优性的一阶必要条件，并利用它构造了梯度流近似算法。该框架的例子与数值模拟。
英文摘要：
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.
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