Recovering Physical Parameters from Fragmented Observations via Exact Distributed Spline Merging
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Computer Science > Machine Learning
arXiv:2609.16579 (cs)
[Submitted on 15 Sep 2026]
Title:Recovering Physical Parameters from Fragmented Observations via Exact Distributed Spline Merging
Authors:Naveen Mysore
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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.
| Comments: | 11 pages, 4 figures, 1 table. Under review at ICLR 2027 |
| Subjects: | Machine Learning (cs.LG); Computational Physics (physics.comp-ph) |
| MSC classes: | 65D07, 62F99, 35R30 |
| ACM classes: | I.2.6; G.1.2; G.3 |
| Cite as: | arXiv:2609.16579 [cs.LG] |
| (or arXiv:2609.16579v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.16579
arXiv-issued DOI via DataCite (pending registration)
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