Dynamics-informed machine learning for recovering extensive missing systems dynamics

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.