{
  "abstract": "A close fit to a scalar time series does not establish either accurate extrapolation or unique mechanistic parameter recovery. We examine a logistic gray-box differential equation coupled to a positive latent suppression state whose relative rate is represented by a bounded neural network. Positivity at every finite time, a population upper bound and a local turning-point criterion are established. For freely chosen bounded closures on a finite observation interval, compatible mechanistic parameters are characterized by a convex feasible set and their nonuniqueness is established. With a positive closure bound, unrestricted positive growth parameters and a free latent initial value, every positive twice continuously differentiable trajectory on that interval is compatible with such a closure. Strictly feasible parameter pairs have two-dimensional feasible neighborhoods. These results describe identifiability boundaries in the freely chosen closure class; a complete structural-identifiability analysis of the fixed finite-width neural architecture remains a separate problem, as does selection of a unique future continuation. Numerical evaluation includes four synthetic mechanisms and current-vintage population estimates for China, India and Japan. Across six historical evaluation windows per country, the gray-box model attains mean training and test absolute percentage errors of 1.126% and 1.338%, respectively. Its mean test error in these windows is below five of the six comparison implementations but above the 0.684% of a residual universal differential equation. Equal additional training of these two models reduces their test errors to 0.714% and 0.409%. The results support conditional usefulness of the latent-suppression structure while demonstrating limitations in optimization, parameter interpretation and temporal generalization.",
  "abstract_shown": true,
  "affiliations": [
    "School of Science, Inner Mongolia University of Technology, Hohhot 010051, China",
    "Department of Mathematics, Shanghai University, Shanghai 200444, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Chenhao Xu"
    },
    {
      "affs": [
        0,
        1
      ],
      "name": "Tiecheng Xia"
    },
    {
      "affs": [
        0
      ],
      "name": "Haijing Ma"
    },
    {
      "affs": [
        0
      ],
      "name": "Junjie Fan",
      "orcid": "0009-0009-4271-4099"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3yd3afznrq28k.bib",
  "cited_by": 0,
  "doi": "10.3390/math14213898",
  "fulltext_url": null,
  "id": "3yd3afznrq28k",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/3898",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7223663511",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/3yd3afznrq28k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14213898",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/3898"
    }
  ],
  "subjects": [
    {
      "field": "medicine",
      "origin": "openalex:2739|Mathematical and Theoretical Epidemiology and Ecology Models",
      "subfield": "epidemiology-public-health"
    }
  ],
  "title": "Positive Latent Suppression in Logistic Neural Differential Equations: Trajectory Reconstruction, Identifiability and Population Hindcasts",
  "title_text": "Positive Latent Suppression in Logistic Neural Differential Equations: Trajectory Reconstruction, Identifiability and Population Hindcasts",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/3yd3afznrq28k",
  "venue": "Mathematics",
  "versions": []
}