aiqbench analysis
This paper introduces MAAT, a novel framework that uses kernel methods and physical priors to reconstruct latent dynamical states from fragmented, noisy scientific measurements. By enforcing constraints like conservation laws within a reproducing kernel Hilbert space, the method enables more robust mechanistic discovery in domains where complete data trajectories are unavailable. The approach demonstrates significant error reduction across diverse benchmarks, including real-world epidemiological modeling.
Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observations
arXiv: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, 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, MAAT substantially reduces trajectory and derivative reconstruction error relative to strong baselines.
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, 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, MAAT substantially reduces trajectory and derivative reconstruction error relative to strong baselines.
Machine Learning (cs.LG)
arXiv:2601.22328 [cs.LG]
(or arXiv:2601.22328v3 [cs.LG] for this version)
Full text under the publisher's open licence · 137 words
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