{
  "id": "2203.04728",
  "version": "v1",
  "published": "2022-03-09T14:07:45.000Z",
  "updated": "2022-03-09T14:07:45.000Z",
  "title": "Dynamic mode decomposition as an analysis tool for time-dependent partial differential equations",
  "authors": [
    "Miha Rot",
    "Martin Horvat",
    "Gregor Kosec"
  ],
  "comment": "6 pages, 8 figures",
  "categories": [
    "math.NA",
    "cs.NA",
    "math.DS",
    "physics.data-an"
  ],
  "abstract": "The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by using scalar reductions, which, however, come with a loss of spatial detail. Dynamic Mode Decomposition is a data-driven analysis method that solves this problem by identifying oscillating spatial structures and their corresponding frequencies. This paper presents the algorithm and provides a physical interpretation of the results by applying the decomposition method to a series of increasingly complex examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-09T14:07:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time-dependent partial differential equations",
      "dynamic mode decomposition",
      "analysis tool",
      "solving partial differential equations",
      "data-driven analysis method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}