{
  "abstract": "Reconstructing physical fields from sparse observations is central to system identification, forecasting, and control, yet sparse measurements generally underdetermine the full field. This makes reconstruction an ill-posed inverse problem rather than simple interpolation. Although many deterministic and generative methods have been developed, there is still no clear consensus on when a single point estimate is sufficient and when a distribution of plausible reconstructions is more useful. We conduct a fair comparison of a deterministic U-Net, conditional diffusion, and prior-guided diffusion under matched experimental settings, including 2D Poisson equation, 2D Navier-Stokes flow, and 1D Kuramoto-Sivashinsky dynamics. Through this comparison, we make three observations. First, accuracy is field- and regime-dependent, with no systematic advantage for diffusion under higher complexity or sparser observations. Second, ensemble means improve phase-aligned accuracy, whereas individual samples better preserve variability and can retain high-wavenumber power in selected regimes. Third, conditional diffusion provides more reliable uncertainty estimates at lower cost, while prior-guided diffusion is more robust to mask-distribution shifts but requires substantially higher inference cost and guidance tuning. These results clarify when generative reconstruction is useful and provide guidance for improving uncertainty estimation, fine-scale sample fidelity, robustness, and computational efficiency in sparse field reconstruction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06135",
  "author_total": 4,
  "authors": [
    {
      "name": "Hao Zhou"
    },
    {
      "name": "Rui Zhang"
    },
    {
      "name": "Qi Wang"
    },
    {
      "name": "Hao Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b7j2ndwfa9p9q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06135",
  "fulltext_url": null,
  "id": "b7j2ndwfa9p9q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06135",
  "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",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7212070602",
  "pdf_url": "https://arxiv.org/pdf/2609.06135",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b7j2ndwfa9p9q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.06135",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06135"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Physical-Field Reconstruction from Sparse Observations: When Are Diffusion Models Preferable to Deterministic Regression?",
  "title_text": "Physical-Field Reconstruction from Sparse Observations: When Are Diffusion Models Preferable to Deterministic Regression?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/b7j2ndwfa9p9q",
  "venue": "arXiv",
  "versions": []
}