Recovering Physical Parameters from Fragmented Observations via Exact Distributed Spline Merging

2026-09-14

AI Summary

本文通过分布式样条合并方法，从分散的观测数据中恢复物理参数，实现了无原始数据共享的精确合并，并应用于实际海洋温度数据。

Abstract

Scientific measurements are frequently distributed across locations, time periods, and institutions. Combining such fragments into a continuous, differentiable field enables recovering governing physical parameters from its derivatives. This paper makes two contributions toward that goal. 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 diffusion coefficient is recovered to 0.11% error and wave speed to 0.12% error; in both cases, distributed merging introduces zero degradation relative to centralized fitting. Application to 41 years of NOAA sea-surface temperature data confirms the result on real spatiotemporal observations.

Problem

• Distributed Observations
• Physical Parameters Recovery
• Spline Merging

Innovation

• distributed spline merging
• fixed-basis ridge-regression
• tensor-product splines
• physical parameter inference
• non-iterative synchronization