A convergence metric for counting statistics in time-resolved small angle neutron scattering

This work introduces a model-independent, dimensionless metric for predicting optimal measurement duration in time-resolved small-angle neutron scattering using early-time data. Built on a Gaussian process regression framework, the method reconstructs scattering profiles with quantified uncertainty, even from sparse or noisy measurements. Demonstrated on the EQ-SANS instrument at the Spallation Neutron Source, the approach generalizes to general SANS instruments with a two-dimensional detector. A key result is the discovery of a dimensionless convergence metric revealing a universal power-law scaling in profile evolution across soft matter systems. When time is normalized by a system-specific characteristic time t*, the variation in inferred profiles collapses onto a single curve with an exponent between -2 and -1. This trend emerges within the first ten time steps, enabling early prediction of measurement sufficiency. The method supports real-time experimental optimization and is especially valuable for maximizing efficiency in low-flux environments such as compact accelerator-based neutron sources.