## 5 Conclusions  
In this study, the application of ML to neutron transmission spectroscopic imaging (NTSI) was investigated using solid-liquid phase fraction analysis as an example. The target of the analysis was the evaluation of the solid-liquid interface movement during the solidification process of LBE. In supervised ML, creating training data can be an issue, but in this study we assembled the training dataset using actual experimental data with a wide variety of solid-liquid phase fractions and crystalline textures of the solid phase without model calculation.  
For the ML analysis, we adopted two steps--the dimensionality reduction of neutron transmission spectrum by PCA and spectrum pattern analysis by KNN--with the goal of reducing the computational cost as much as possible. For the examination of this ML analysis, the evaluating spectrum dataset was created by first setting the phase fraction between the simulated solid spectra and experimental liquid spectrum. Then, the ML was  
Figure 16: Solidification velocity estimated from the averaged solidification interface position obtained by ML analysis.  
Figure 15: Time dependence of the averaged solid–liquid interface position (50% solid-phase fraction) according to ML analysis. The interface position estimated from the neutron transmission image is also shown as a comparison [26; 27].  
examined with a dataset that contained Gaussian distributed random errors to simulate statistical errors. As a result, it was found that PCA can evaluate the solid-liquid phase fraction of LBE with principal components up to several dimensions, while KNN can evaluate the fraction with the same accuracy as that found for the training data.  
As a result of applying this ML analysis to the actual experimental data, it was possible to evaluate the solid-, liquid-, and mixed-interface zones quantitatively based on the phase fraction. The average position of the solid-liquid interface was generally consistent with the results of a previous study [26, 27]. The ML analysis introduced here was for the simple problem of shape recognition about the mixture of the spectra of solid- and liquid-phases, which have clearly different shapes. To extend ML to general spectrum analysis, there are many issues such as accumulation of training data. We are considering applying ML to NTSI spectral analysis by limiting the number of parameters of the crystal texture.  
Thus, the application of ML analysis to NTSI seems to have potential. In unsupervised ML, the visualization of PCA results is also expected to be a bridge to detailed crystallographic analysis because it can clearly show the characteristics of the transmission spectrum. Further, the result that the measured spectra can be used as the training data in supervised ML is advantageous to the NTSI, which can collect the number of spectra with multiple pixels on a two-dimensional detector. The effectiveness of the use of experimental spectra for training data, as revealed in this study, shows the potential of ML analysis using large databases of previous experimental data for new experimental data.  
Conceptualization, T.K., K.H. and H.S.; methodology, T.K., K.H., H.S., K.O. and Y.S.([PERSON]); software, K.H.; validation, T.K. and H.S.; formal analysis, T.K., K.H. and H.S.; investigation, H.S., D.I. and Y.S.([PERSON]); resources, D.I. and Y.S.([PERSON]); data curation, T.K. and K.H.; writing - original draft, T.K.; writing - review & editing, K.H., H.S., K.O., Y.S.([PERSON]), D.I. and Y.S.([PERSON]); visualization, T.K., K.H. and H.S.; supervision, T.K. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors would like to thank [PERSON] (J-PARC) and the J-PARC ML BL22 RADEN group members for their assistance with the experiment.  
The authors declare no conflict of interest.