{
  "abstract": "Inevitable missing values in observational time series often hinder reliable data-driven modeling of complex systems across diverse domains. Recovery is essential yet challenging, particularly in high-dimensional systems where most variables can exhibit extensive intra-series missingness and widespread inter-variable missingness simultaneously. In this study, we introduce a dynamics-informed imputation framework, termed Full-Partial Reconstruction Mapping (FPRM). In contrast to traditional approaches that directly fit time series interdependences, the FPRM embeds intrinsic dynamical priors via state-space reconstruction and recovers multiple incomplete series by learning diffeomorphic topology between attractors from complete and incomplete data. We validate the FPRM on paradigmatic model systems (e.g., an ecology system, the ordinary Lorenz system, a coupled 120-dimensional (120D) Lorenz system, and a coupled 120D Rössler system and real-world datasets (e.g., road occupancy rate from transportation system, electroencephalogram (EEG) signals from neuroscience, exchange rates from finance, and wind speed from climate systems). Even in high-dimensional systems where only one variable is fully observed and all others suffer from extreme missingness (e.g., 90%), the FPRM enables reliable imputation of multiple incomplete variables-a task that challenges most existing approaches. This dynamics-guided framework outperforms traditional approaches, alleviating substantial data gaps and enabling robust data-driven paradigms for complex dynamical systems.",
  "abstract_shown": true,
  "affiliations": [
    "College of Management Science, Chengdu University of Technology, Chengdu, China. wutaopj@163.com.",
    "International Research Center for Neurointelligence (IRCN), The University of Tokyo, Tokyo, Japan. wutaopj@163.com.",
    "School of Economics and Management, China University of Geosciences, Beijing, China. gxy5669777@126.com.",
    "MOE Social Science Laboratory of Mineral Resources Security Governance, China University of Geosciences, Beijing, China. gxy5669777@126.com.",
    "Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China.",
    "Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China, Chengdu, China.",
    "School of Economics and Management, Beijing University of Chemical Technology, Beijing, China.",
    "School of Advanced Manufacturing and Robotics, Peking University, Beijing, China.",
    "International Research Center for Neurointelligence (IRCN), The University of Tokyo, Tokyo, Japan.",
    "School of Economics and Management, China University of Geosciences, Beijing, China. ahz369@163.com.",
    "MOE Social Science Laboratory of Mineral Resources Security Governance, China University of Geosciences, Beijing, China. ahz369@163.com.",
    "Center for Mineral Industrial Chains, Hebei GEO University, Shijiazhuang, China. ahz369@163.com.",
    "Potsdam Institute for Climate Impact Research (PIK)-Member of the Leibniz Association, Potsdam, Germany. kurths@pik-potsdam.de."
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 8,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Tao Wu",
      "orcid": "0000-0002-8131-1243"
    },
    {
      "affs": [
        2,
        3
      ],
      "name": "Xiangyun Gao",
      "orcid": "0000-0003-2101-1609"
    },
    {
      "affs": [
        4,
        5
      ],
      "name": "Ying Tang"
    },
    {
      "affs": [
        6
      ],
      "name": "Feng An"
    },
    {
      "affs": [
        7
      ],
      "name": "Xiaotian Sun"
    },
    {
      "affs": [
        8
      ],
      "name": "Kazuyuki Aihara",
      "orcid": "0000-0002-4602-9816"
    },
    {
      "affs": [
        9,
        10,
        11
      ],
      "name": "Haizhong An"
    },
    {
      "affs": [
        12
      ],
      "name": "Jürgen Kurths",
      "orcid": "0000-0002-5926-4276"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fq0q6acn6zd2g.bib",
  "cited_by": 0,
  "doi": "10.1038/s41467-026-77922-1",
  "fulltext_url": "https://europepmc.org/articles/PMC13683343",
  "id": "fq0q6acn6zd2g",
  "issns": [
    "2041-1723"
  ],
  "landing_url": "https://europepmc.org/article/MED/42901974",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7131882012",
  "pdf_url": "https://europepmc.org/articles/PMC13683343?pdf=render",
  "pmcid": "PMC13683343",
  "pmid": "42901974",
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fq0q6acn6zd2g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:41Z",
      "native_id": "MED:42901974",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42901974"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3109|Model Reduction and Neural Networks",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Dynamics-informed machine learning for recovering extensive missing systems dynamics.",
  "title_text": "Dynamics-informed machine learning for recovering extensive missing systems dynamics.",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:19:41Z",
  "url": "https://research.draconitic.com/paper/fq0q6acn6zd2g",
  "venue": "Nature communications",
  "versions": []
}