# Data-Driven Approximation of the Perron-Frobenius Operator Using the Wasserstein Metric

arXiv: https://arxiv.org/abs/2011.00759 · HTML: https://mlsanity.com/paper/2011.00759/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2020.

## Built on by (most cited first, 2 of 2)

- [Perron--Frobenius Operator Matching for Generative Modeling](https://mlsanity.com/paper/2606.17465/) (2026)
- [Functional dynamic mode decomposition: Learning infinite-dimensional systems from data](https://mlsanity.com/paper/2609.29159/) (2026)

## Abstract (arXiv)

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.