{
  "id": "2312.02067",
  "version": "v1",
  "published": "2023-12-04T17:26:49.000Z",
  "updated": "2023-12-04T17:26:49.000Z",
  "title": "Learning Feynman integrals from differential equations with neural networks",
  "authors": [
    "Francesco Calisto",
    "Ryan Moodie",
    "Simone Zoia"
  ],
  "comment": "27 pages, 9 figures, 3 tables",
  "categories": [
    "hep-ph",
    "hep-th"
  ],
  "abstract": "We present a new approach for evaluating Feynman integrals numerically. We apply the recently-proposed framework of physics-informed deep learning to train neural networks to approximate the solution to the differential equations satisfied by the Feynman integrals. This approach relies neither on a canonical form of the differential equations, which is often a bottleneck for the analytical techniques, nor on the availability of a large dataset, and after training yields essentially instantaneous evaluation times. We provide a proof-of-concept implementation within the PyTorch framework, and apply it to a number of one- and two-loop examples, achieving a mean magnitude of relative difference of around 1% at two loops in the physical phase space with network training times on the order of an hour on a laptop GPU.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-04T17:26:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "differential equations",
      "learning feynman integrals",
      "train neural networks",
      "yields essentially instantaneous evaluation times"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}