{
  "id": "2011.00759",
  "version": "v1",
  "published": "2020-11-02T05:59:32.000Z",
  "updated": "2020-11-02T05:59:32.000Z",
  "title": "Data-Driven Approximation of the Perron-Frobenius Operator Using the Wasserstein Metric",
  "authors": [
    "Amirhossein Karimi",
    "Tryphon T. Georgiou"
  ],
  "comment": "11 pages",
  "categories": [
    "math.OC",
    "cs.SY",
    "eess.SY"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-02T05:59:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E12",
      "93E35",
      "49J45",
      "49Q20",
      "49M29",
      "90C46"
    ],
    "keywords": [
      "perron-frobenius operator",
      "wasserstein metric",
      "data-driven approximation",
      "gradient flow approximating algorithm",
      "first-order necessary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}