{
  "abstract": "When reconstructing the hidden state of a partial differential equation (PDE) system from partial observations, aggregate prediction error measures performance on a given data distribution but does not reveal how strongly the observations constrain each predicted direction. We introduce UniPDE-Bench, a direction-wise evaluation protocol that incorporates local observation geometry into state-estimation assessment, providing a reference for prediction recovery and confidence-based selection that is independent of the estimator. The protocol whitens the joint observation Jacobian by the noise covariance and normalizes it by a state metric. Its complete right singular basis represents joint variations of the state, which a relative sensitivity threshold partitions into retained and below-threshold directions. In this common basis, the protocol evaluates recovery and the agreement between prediction claims and the geometric partition, while recovery and abstention curves describe confidence-based selection at different claim coverages. In the simulated tasks and observation configurations studied here, confidence rules whose overall ranking exceeds chance can still exhibit below-random abstention on below-threshold directions at some high claim coverages. By separating empirical recovery from direction-selection quality, the protocol relates prediction performance to local observation sensitivity and provides an evaluation of partially observed state estimators beyond aggregate error.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12493",
  "author_total": 6,
  "authors": [
    {
      "name": "Qingwei Dong"
    },
    {
      "name": "Peng Zeng"
    },
    {
      "name": "Guangxi Wan"
    },
    {
      "name": "Jiyuan Zhang"
    },
    {
      "name": "Ruikai Liu"
    },
    {
      "name": "Yuqi Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1mrfh1yjezs04.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12493",
  "fulltext_url": null,
  "id": "1mrfh1yjezs04",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12493",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7212809376",
  "pdf_url": "https://arxiv.org/pdf/2609.12493",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1mrfh1yjezs04.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:17Z",
      "native_id": "2609.12493",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12493"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Recoverability Is a Subspace Property: A Benchmark for Certified State Estimation from Partial PDE Observations",
  "title_text": "Recoverability Is a Subspace Property: A Benchmark for Certified State Estimation from Partial PDE Observations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:17Z",
  "url": "https://research.draconitic.com/paper/1mrfh1yjezs04",
  "venue": "arXiv",
  "versions": []
}