{
  "id": "1906.06782",
  "version": "v1",
  "published": "2019-06-16T22:00:12.000Z",
  "updated": "2019-06-16T22:00:12.000Z",
  "title": "Meta-learning Pseudo-differential Operators with Deep Neural Networks",
  "authors": [
    "Jordi Feliu-Faba",
    "Yuwei Fan",
    "Lexing Ying"
  ],
  "comment": "20 pages, 8 figures",
  "categories": [
    "math.NA",
    "cs.LG",
    "cs.NA"
  ],
  "abstract": "This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-differential operators can be approximated in a compressed form with a collection of vectors. The nonlinear map from the parameter to this collection of vectors and the wavelet transform are learned together from a small number of matrix-vector multiplications of the pseudo-differential operator. Numerical results for Green's functions of elliptic partial differential equations and the radiative transfer equations demonstrate the efficiency and accuracy of the proposed approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-16T22:00:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deep neural networks",
      "meta-learning pseudo-differential operators",
      "elliptic partial differential equations",
      "radiative transfer equations demonstrate",
      "nonstandard wavelet form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}