{
  "abstract": "We develop a mesh-free neural JKO scheme for advection-reaction-diffusion equations with a gradient-flow structure in the Hellinger-Kantorovich (HK) geometry of unbalanced optimal transport. Each update is parametrized by a spatial map and a mass-changing factor, allowing spatial redistribution and local mass creation or loss to be treated jointly within a single variational step. Their cone action bounds the squared HK distance from above, yielding a sufficient condition for discrete energy dissipation through comparison with the identity pair. Minimizing the pair objective over all admissible pairs recovers the exact JKO minimum when the source and a minimizer have positive densities. We establish existence and mass bounds for JKO minimizers and, under additional assumptions, obtain positivity and regularity together with a discrete Euler-Lagrange equation and a metric-dissipation identity. The self-consistent chemical potential is then nonincreasing along an optimal map. There exist parametric pairs whose endpoint densities and objective values converge to those of an exact JKO minimizer, provided a regular-pair approximation hypothesis holds. Finally, we show that a primal-dual gap controls objective suboptimality and, for Boltzmann entropy, the $L^1$ density error, assuming exact-step regularity, positive-semidefinite interactions, and global dual feasibility. Numerical experiments examine pointwise agreement with the PDE, energy dissipation, and the roles of transport, reaction, and fully implicit interactions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07602",
  "author_total": 4,
  "authors": [
    {
      "name": "Geuntaek Seo"
    },
    {
      "name": "Cheolhyeong Kim"
    },
    {
      "name": "Hwijae Son"
    },
    {
      "name": "Hyung Ju Hwang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ksbq2vbfskw0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07602",
  "fulltext_url": null,
  "id": "4ksbq2vbfskw0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07602",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.07602",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ksbq2vbfskw0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07602",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07602"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Neural JKO Scheme for Hellinger-Kantorovich Gradient Flows via Monge-Growth Pairs",
  "title_text": "A Neural JKO Scheme for Hellinger-Kantorovich Gradient Flows via Monge-Growth Pairs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/4ksbq2vbfskw0",
  "venue": "arXiv",
  "versions": []
}