Correlation-aware binning for small-angle neutron scattering via Gaussian-process inference

Tung, C.-H.; Do, C.; Jang, J.; Lee, S.; Huang, G.-R.; Porcar, L.; Wang, Y.; Shinohara, Y.; Chen, W.-R.

doi:10.1107/S1600576726000907

Journal of Applied Crystallography Journal of Applied
Crystallography

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Figure 5
Verification of the universal scaling behavior across different scattering systems. (a) Normalized mean-squared error $[{\cal E}/{\cal E}_{0}]$ plotted against total detector counts n. GP-processed results (blue symbols) from all instruments and materials collapse onto a single $[n^{-4/5}]$ master curve, while conventional binning without correlation correction (red symbols) follows the $[n^{-1}]$ scaling predicted by the CLT. The red dotted horizontal lines indicate the precision floor defined by the instrumental bin width. (b) Ratio $[{\cal E}/{\cal E}_{{\rm opt}}^{{\rm GPR}}]$ , showing that GP postprocessing consistently yields lower error than conventional approaches. Blue dashed lines mark the theoretical limit, demonstrating the robustness of the $[n^{-4/5}]$ scaling law across various SANS and USANS data sets, including PEG-b-PLAyne-b-PLA, G5 dendrimers, polymer melts, PL-HA aggregates, conjugated polymers (P3AT), ionic peptides, and PAMAM/DBSA and CTAB/NaSal systems.

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 59| Part 2| April 2026| Pages 334-342

https://doi.org/10.1107/S1600576726000907

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