{
  "abstract": "Bifurcations are ubiquitous in physical systems, from structural buckling to fluid and climate dynamics, yet they remain largely unexplored in deep learning. At a symmetry-breaking bifurcation, a single input admits multiple equally valid solutions, violating the one-to-one assumption underlying most learned physical surrogates. We introduce Bi-FORK, a generative framework for learning these one-to-many solution maps in high-dimensional systems. Bi-FORK generates complete trajectories through latent flow matching, preserving space and time coherence, and uses repulsion-guided sampling to recover distinct solution branches in a single amortized pass. We evaluate Bi-FORK on buckling beams, mechanical metamaterials, and Allen-Cahn phase separation, spanning continuous, discrete, and field-valued bifurcations with discretizations up to 260,000 points. Bi-FORK recovers the multimodal solution structure while scaling several orders of magnitude beyond prior approaches, opening generative modeling to high-dimensional bifurcating physical systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12449",
  "author_total": 7,
  "authors": [
    {
      "name": "Anna Zimmel"
    },
    {
      "name": "Fleur Hendriks"
    },
    {
      "name": "Markus Holzleitner"
    },
    {
      "name": "Florian Sestak"
    },
    {
      "name": "Martin Weichselbaumer"
    },
    {
      "name": "Vlado Menkovski"
    },
    {
      "name": "Johannes Brandstetter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fgq727y57xpz5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12449",
  "fulltext_url": null,
  "id": "fgq727y57xpz5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12449",
  "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.AI"
    ],
    [
      "arxiv",
      "cs.CE"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7221171296",
  "pdf_url": "https://arxiv.org/pdf/2610.12449",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fgq727y57xpz5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.12449",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12449"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems",
  "title_text": "Bi-FORK: Generative Modeling of High-Dimensional Bifurcating Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/fgq727y57xpz5",
  "venue": "arXiv",
  "versions": []
}