Data-Driven Approximation of the Perron-Frobenius Operator Using the Wasserstein Metric
Optimization and Control
2020-11-03 v1 Systems and Control
Systems and Control
Abstract
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.
Cite
@article{arxiv.2011.00759,
title = {Data-Driven Approximation of the Perron-Frobenius Operator Using the Wasserstein Metric},
author = {Amirhossein Karimi and Tryphon T. Georgiou},
journal= {arXiv preprint arXiv:2011.00759},
year = {2020}
}
Comments
11 pages