{
  "abstract": "While the inverse heat dissipation model has shown success in image generation, it is intrinsically ill-posed. To address this issue, we introduce a quasi-reversibility regularization technique and propose a quasi-reversibility-regularized inverse heat dissipation model. We derive the variational formulation of the objective function for the proposed model and establish an upper bound on the error between the regularized solution obtained from noisy observations and the exact solution in the relevant function space. These findings provide a theoretical basis for improving inverse heat dissipation models. The experimental results demonstrate that compared with the original inverse heat dissipation model, the new model achieves an 34.6% reduction in Fréchet Inception Distance on the MNIST dataset.",
  "abstract_shown": true,
  "affiliations": [
    "School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China",
    "Department of Statistics, Hangzhou Dianzi University, Hangzhou 310018, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Zhiqi Tong"
    },
    {
      "affs": [
        0
      ],
      "name": "Zheng Han"
    },
    {
      "affs": [
        1
      ],
      "name": "Qinghua Hu"
    },
    {
      "affs": [
        1
      ],
      "name": "Jing Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgkp19s938687.bib",
  "cited_by": 0,
  "doi": "10.3390/math14213965",
  "fulltext_url": null,
  "id": "bgkp19s938687",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/3965",
  "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": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/bgkp19s938687.ris",
  "sources": [
    {
      "first_seen": "2026-10-31T00:20:46Z",
      "native_id": "10.3390/math14213965",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/3965"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Variational Inference and Error Estimation for Inverse Heat Dissipation Models with Quasi-Reversibility Regularization",
  "title_text": "Variational Inference and Error Estimation for Inverse Heat Dissipation Models with Quasi-Reversibility Regularization",
  "type": "peer-reviewed",
  "updated_at": "2026-11-01T00:20:44Z",
  "url": "https://research.draconitic.com/paper/bgkp19s938687",
  "venue": "Mathematics",
  "versions": []
}