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

Authors :
Karimi, Amirhossein
Georgiou, Tryphon T.
Publication Year :
2020

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.<br />Comment: 11 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2011.00759
Document Type :
Working Paper