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

Amirhossein Karimi; Tryphon T. Georgiou

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arXiv · 2011.00759

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

Amirhossein Karimi·Tryphon T. Georgiou

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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.

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BibTeX RIS

Amirhossein Karimi, Tryphon T. Georgiou. 2020-11-02. Data-Driven Approximation of the Perron-Frobenius Operator Using the Wasserstein Metric. https://arxiv.org/abs/2011.00759

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