Automatic Termination Strategy of Inelastic Neutron-scattering Measurement Using Bayesian Optimization for Bin-width Selection

Kensuke Muto; Hirotaka Sakamoto; Kenji Nagata; Taka-hisa Arima; Masato Okada

physics.data-anMar 16, 2026

Automatic Termination Strategy of Inelastic Neutron-scattering Measurement Using Bayesian Optimization for Bin-width Selection

Authors: Kensuke Muto, Hirotaka Sakamoto, Kenji Nagata, Taka-hisa Arima, Masato Okada

Organizations: Graduate School of Frontier Sciences, The University of Tokyo, Chiba 277–0882, Japan · Karakuri, Inc., 2-7-3 Tsukiji, Chuo-ku, Tokyo 104-0045, Japan · Research and Services Division of Materials Data and Integrated System, National Institute for Materials Science, Tsukuba, Ibaraki 305–0047, Japan · Graduate School of Frontier Sciences, The University of Tokyo, Chiba 277–8561, Japan

Abstract

Currently, an excessive amount of event data is being obtained in four-dimensional inelastic neutron-scattering experiments. A method for automatic bin-width optimization of multidimensional histograms has been developed and recently validated on real inelastic neutron-scattering data. However, measuring beyond the equipment resolution leads to inefficient use of valuable beam time. To improve experimental efficiency, an automatic termination strategy is essential. We propose a Bayesian-optimization-based method to compute a stopping criterion that can support online decisions on whether to continue or terminate an experiment. In the proposed method, the bin-width optimization is performed using Bayesian optimization to efficiently compute the optimal bin widths. The experiment is terminated when the optimal bin widths become smaller than the target resolutions. In numerical experiments using real inelastic neutron-scattering data, the optimal bin widths decrease as the number of events increases. Even the optimal bin widths for data downsampled to 1/5 are comparable with the resolutions limited by the sample size, choppers, and so on. This implies excessive measurement of the inelastic neutron experiments for the moment. Moreover, we found that Bayesian optimization can reduce the search cost to approximately 10% of an exhaustive search in our numerical experiments.

Figures & tables

Fig. 1: Overview of the termination strategy.

Fig. 2: Overview of the summed-area tables algorithm for the 2D case. We set a sufficient fine histogram and call it “raw” count data $a_{i,j}$ .

Panel of Figure 3 — Fig. 3: 2D slices of 4D inelastic neutron-scattering count data. Regarding (a), $q_{y}$ and $q_{z}$ are fixed at $0.4845\pm 0.0323$ and $0.0323\pm 0.0323$ , respectively. Regarding (b), $q_{x}$ and $q_{z}$ are fixed at $0.6137\pm 0.0323$ and $0.6137\pm 0.0323$ , respectively. Regarding (c), $E$ and $q_{y}$ are fixed at $1.75\pm 0.25$ and $0.6137\pm 0.0323$ , respectively. The upper bound of the color axes is set to 2.

Panel of Figure 4 — Fig. 4: 1D slices of 4D cost functions computed by changing the downsampling rate of $r_{ds}$ . To unify the scale, each cost function is divided by the square of the number of events. (a)–(d) represent landscapes of the cost functions in the $E$ , $q_{x}$ , $q_{y}$ , and $q_{z}$ direction. The cost value in one axis direction is visualized, and the other three axis directions are fixed to the optimal bin width. The optimal bin widths $(\Delta_{E},\Delta_{q_{x}},\Delta_{q_{y}},\Delta_{q_{z}})$ are $(4{\rm[meV]},0.32,0.26,0.32)$ for $r_{ds}=0.1$ , $(4{\rm[meV]},0.19,0.13,0.32)$ for $r_{ds}=0.2$ , $(3{\rm[meV]},0.13,0.13,0.19)$ for $r_{ds}=0.5$ , and $(2{\rm[meV]},0.13,0.13,0.13)$ for $r_{ds}=1$ . Approximate optimal bin widths and the experiment’s resolutions are represented as filled circles and dashed lines.

Panel of Figure 5 — Fig. 5: Performance of BO search in bin width selection for each $r_{ds}$ . The predictive distribution of GP was used to compute the acquisition function. $100$ experiments were performed on the same event datasets with different initial $(\Delta_{E},\Delta_{qx},\Delta_{qy},\Delta_{qz})$ points. The distribution of minimum values of the cost function $min(C)$ for each experiment is plotted as a function of the iteration number. Here, the baseline is set to the global minimum of the cost function $C_{\text{global minima}}$ . Box plotlines show $25$ th, median, and $75$ th percentile from the bottom of the box to top. Whisker length is set to 0. Data points outside the boxes are plotted as dots.

Fig. 6: Comparison of computational costs of the BO search (

cost_{\rm BO}

) with that of an exhaustive search of all

10,000

points (

cost_{\rm 10,000}

) for three sample numerical experiments by referring to the sequence of searched points. “BO” represents the computational cost of the acquisition function calculation only. trial 1-3 include both acquisition function computation time and cost function evaluation. At 500 iterations, trial 1, trial 2, and trial 3 reached 10.9%, 9.3%, and 10.2% respectively. It took about 3.86 hours to conduct an exhaustive search of

10,000

points. (CPU: Apple M1 Max; memory: 32 GB).

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When Has a Bayesian Neural Network Sampled Enough? Adaptive Inference Time with Statistical Guarantees

Fabian Denoodt, Sibylle Hess

Eindhoven University of Technology

Adaptive Sampling Bayesian Neural Networks Efficient Neural Network Inference

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Bayesian neural network predictions are commonly approximated using a fixed number of Monte Carlo samples per input, without controlling the resulting error that comes from this finite sample. We propose the use of confidence sequences to dynamically determine how many samples are needed while maintaining statistical guarantees. We consider several ways in which predictive probabilities are used, including identifying the most likely class, approximating the full predictive distribution, and resolving probability-threshold decisions. Sampling stops once the corresponding decision can be made with the desired guarantee. Experiments show that the method allocates the computational budget efficiently, assigning more samples to ambiguous inputs than to easy inputs while preserving reliable decisions and reducing overall latency relative to a fixed Monte Carlo budget.

Abstract

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