Dynamics-informed machine learning for recovering extensive missing systems dynamics.
13 affiliations
- 1College of Management Science, Chengdu University of Technology, Chengdu, China. [email protected].
- 2International Research Center for Neurointelligence (IRCN), The University of Tokyo, Tokyo, Japan. [email protected].
- 3School of Economics and Management, China University of Geosciences, Beijing, China. [email protected].
- 4MOE Social Science Laboratory of Mineral Resources Security Governance, China University of Geosciences, Beijing, China. [email protected].
- 5Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China.
- 6Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China, Chengdu, China.
- 7School of Economics and Management, Beijing University of Chemical Technology, Beijing, China.
- 8School of Advanced Manufacturing and Robotics, Peking University, Beijing, China.
- 9International Research Center for Neurointelligence (IRCN), The University of Tokyo, Tokyo, Japan.
- 10School of Economics and Management, China University of Geosciences, Beijing, China. [email protected].
- 11MOE Social Science Laboratory of Mineral Resources Security Governance, China University of Geosciences, Beijing, China. [email protected].
- 12Center for Mineral Industrial Chains, Hebei GEO University, Shijiazhuang, China. [email protected].
- 13Potsdam Institute for Climate Impact Research (PIK)-Member of the Leibniz Association, Potsdam, Germany. [email protected].
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.
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BibTeX
@article{wu2026dynamicsinformed,
title = {{Dynamics-informed machine learning for recovering extensive missing systems dynamics.}},
author = {Tao Wu and Xiangyun Gao and Ying Tang and Feng An and Xiaotian Sun and Kazuyuki Aihara and Haizhong An and Jürgen Kurths},
journal = {Nature communications},
year = {2026},
month = sep,
doi = {10.1038/s41467-026-77922-1},
url = {https://europepmc.org/article/MED/42901974},
note = {CC BY},
}
RIS
TY - JOUR
TI - Dynamics-informed machine learning for recovering extensive missing systems dynamics.
AU - Tao Wu
AU - Xiangyun Gao
AU - Ying Tang
AU - Feng An
AU - Xiaotian Sun
AU - Kazuyuki Aihara
AU - Haizhong An
AU - Jürgen Kurths
PY - 2026
DA - 2026/09/19
JO - Nature communications
DO - 10.1038/s41467-026-77922-1
UR - https://europepmc.org/article/MED/42901974
AB - 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.
SN - 2041-1723
ER -