Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observations

תקציר מקורי באנגליתarXiv:2601.22328v3 Announce Type: replace Abstract: 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 MAAT (Model Aware Approximation of Trajectories), a framework for knowledge-informed Kernel State Reconstruction in partially observed dynamical systems. 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, pro