从碎片化观测中通过精确分布式样条合并恢复物理参数
Recovering Governing Dynamics from Distributed Observations via Exact Spline Merging
- University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
- Dyssonance AI
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种精确分布式样条合并方法，从碎片化观测中恢复物理参数，无需共享原始数据，误差低于0.12%，并在真实海温数据上验证。
AI中文摘要：
科学测量经常分布在不同的地点、时间段和机构中。将这些碎片组合成一个连续、可微的场，可以从其导数中恢复控制物理参数。本文为实现这一目标做出了两项贡献。首先，将固定基岭回归统计的既定加性结构应用于张量积样条场：每个数据持有者计算局部Gram矩阵和矩向量，合并后的解在数学上与集中式拟合相同，无需共享原始数据，也无需迭代同步。这一性质特定于固定特征平方误差设置；当前的推导并未为一般联合训练的多层网络建立类似的保证。其次，一个完整的流程通过场重建、导数提取和线性回归将分布式观测连接到物理参数推断。扩散系数的恢复误差为0.11%，波速的恢复误差为0.12%；在两种情况下，分布式合并相对于集中式拟合引入了零退化。对41年NOAA海面温度数据的应用证实了该结果在真实时空观测上的有效性。
英文摘要：
Scientific observations are frequently distributed across locations, time periods, and institutions. Combining such observations into a continuous, differentiable field enables recovering governing physical parameters from its derivatives. This paper makes two contributions in this setting. First, the established additive structure of fixed-basis ridge-regression statistics is applied to tensor-product spline fields: each data holder computes a local Gram matrix and moment vector, and the merged solution is mathematically identical to centralized fitting, with no raw data shared and no iterative synchronization. This property is specific to the fixed-feature squared-error setting; the present derivation does not establish an analogous guarantee for general jointly trained multilayer networks. Second, a complete pipeline connects distributed observations to physical parameter inference through field reconstruction, derivative extraction, and linear regression. The pipeline is validated on four PDEs: diffusion, wave, heat-with-source, and the nonlinear viscous Burgers equation, recovering governing parameters to sub-percent accuracy in the linear cases and 5\% for Burgers. In all cases, distributed merging introduces zero degradation relative to centralized fitting. Synthetic experiments validate parameter recovery; application to 41 years of NOAA sea-surface temperature data validates field reconstruction and aggregation equivalence on real spatiotemporal observations. Source code to reproduce all experiments is available at https://github.com/NAVEENMN/splinemerge.
