从零散观测中重建动态系统状态，提升物理一致性与精度
Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observations
- 在再生核希尔伯特空间中建模，融合多种观测算子与先验知识
- 在9个科学基准上误差显著低于基线，真实新冠数据表现优异
- 适合需要精准状态估计的机制发现任务，如符号回归
现实世界的科学系统很少能通过完整、规律采样的状态轨迹进行观测。相反，测量常是部分的、含噪的且异质的，仅提供对隐藏动力学状态的碎片化视图。我们提出MAAT（Model Aware Approximation of Trajectories）框架，用于在部分观测的动力系统中进行知识引导的核空间状态重建。MAAT在再生核希尔伯特空间中构建重建模型，整合异质观测算子及语义与结构先验，包括非负性、守恒约束和领域特定的测量模型。该方法生成平滑且符合物理规律的状态估计，并提供解析时间导数，为碎片化测量与下游机制发现方法（如符号回归）之间建立原则性接口。在九个科学基准、多种噪声场景以及一个真实世界新冠数据集上，MAAT相比强基线显著降低了轨迹与导数的重建误差。
原文摘要 · Abstract (English)
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.
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