Distributed method merges fragmented data to find physical parameters accurately
Recovering Physical Parameters from Fragmented Observations via Exact Distributed Spline Merging
Machine Learning
Summary
Many scientific measurements come from different places and times, making it hard to combine them smoothly. The authors developed a way for separate holders of data to work together without sharing raw data, yet still get the same result as if all data were combined centrally. Their method reconstructs smooth physical fields and extracts key parameters like how heat diffuses or how waves travel with very high accuracy. They tested this with decades of sea temperature data, showing it works well on real-world messy data.
What this means in practice
- •For environmental data teams: Combine fragmented environmental sensor readings to accurately estimate physical parameters like diffusion without sharing raw data.
- •For weather modelers: Merge distributed observational datasets to create smooth fields and precisely recover wave speed and diffusion parameters for improved model inputs.
Authors
Naveen Mysore
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.