{
  "abstract": "This work is concerned with the numerical computation of Gross-Pitaevskii ground states using the tensor train (TT) format. We regard the problem as the minimization of the Gross-Pitaevskii energy functional under a unit mass constraint, and propose a first-order Riemannian optimization scheme that preserves both the mass constraint and the low-rank representation throughout the optimization, by operating on the manifold of unit-norm functions of fixed TT-rank. On this manifold, we derive the energy-adaptive Riemannian gradient and show how to compute it efficiently in the TT format. Spatial discretization is performed using a spectral method with numerical integration, which allows the required computations to be carried out efficiently while preserving the low-rank format. The method is shown to substantially reduce computational time compared to full-rank computations, while maintaining accuracy for both single- and multicomponent Gross-Pitaevskii equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37103",
  "author_total": 3,
  "authors": [
    {
      "name": "Ivan Bioli"
    },
    {
      "name": "Carlo Marcati"
    },
    {
      "name": "Maxim Rakhuba"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4q0hywwvmqd7v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37103",
  "fulltext_url": null,
  "id": "4q0hywwvmqd7v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37103",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2605|Tensor decomposition and applications"
    ]
  ],
  "openalex": "W7214927422",
  "pdf_url": "https://arxiv.org/pdf/2609.37103",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4q0hywwvmqd7v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37103",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37103"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Riemannian optimization on low-rank tensor train manifolds for the Gross-Pitaevskii equation",
  "title_text": "Riemannian optimization on low-rank tensor train manifolds for the Gross-Pitaevskii equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/4q0hywwvmqd7v",
  "venue": "arXiv",
  "versions": []
}