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

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 stopping criteria and determine whether to continue or terminate the experiment in real time. 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 (6)

• Figure 1: Overview of the termination strategy.
• Figure 2: Overview of the summed-area tables algorithm for the 2D case. We set a sufficient fine histogram and call it "raw" count data $a_{i,j}$.
• Figure 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.
• Figure 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.
• Figure 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.