Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observations

Real-world scientific systems are rarely observed through complete, regularly sampled state trajectories. Instead, measurements are often partial, noisy, and heterogeneous, providing fragmented views of latent dynamical states. We introduce $\texttt{MAAT}$ (Model Aware Approximation of Trajectories), a framework for knowledge-informed Kernel State Reconstruction in partially observed dynamical systems. $\texttt{MAAT}$ formulates reconstruction in a reproducing kernel Hilbert space and incorporates heterogeneous observation operators together with semantic and structural priors, including non-negativity, conservation constraints, and domain-specific measurement models. This yields smooth, physically consistent state estimates with analytic time derivatives, providing a principled interface between fragmented measurements and downstream mechanistic discovery methods such as symbolic regression. Across nine scientific benchmarks, multiple noise regimes, and a real-world COVID-19 dataset, $\texttt{MAAT}$ substantially reduces trajectory and derivative reconstruction error relative to strong baselines.