## 4 Machine Learning Analysis Based on Actual Measurement Data
### Solid-Liquid Phase Fraction Imaging of LBE Using Supervised Machine Learning Analysis  
Figure 12 shows an example of a single-pixel spectrum used for analysis. It was estimated to be the liquid phase from the thermocouple measurement until 30 min after the solidification process started. The statistical error is large for one-pixel data. Such a spectrum was created pixel by pixel from the TOF transmission image data, and the solid-phase fraction was quantitatively obtained by KNN analysis. Figure 13 shows an example of the result of quantifying the solid-phase fraction, performed on the entire detection area. The linear shadows shown by the blue arrows are thermocouples. To exclude the influence of the background caused by such devices, the solidification process was evaluated in the zone indicated by the red frame. Note that, once the spectral dataset for analysis is prepared, the KNN analysis can be completed in a few minutes, so the effect of time efficiency is extremely high.  
Figure 12: Example of neutron transmission spectrum analyzed by ML analysis. It shows one-pixel data of the liquid-phase zone from the start of the solidification process to 30 min later.  
Figure 13: An example of solid–liquid phase fraction imaging (80 mm \(\times\) 80 mm) results obtained by ML analysis (at the beginning of the solidification process). The black shadows at the blue arrow positions in the figure are the thermocouples in the sample. To eliminate the influence of the thermocouples and the insulation material around the sample container, the data inside the red frame were used for the analysis to determine the movement of the solid–liquid interface.  
Some examples of the solid-phase fraction map and average in the horizontal direction inside the red-frame zone are shown in Figure 14. In the average diagram on the right in the figure, the horizontal axis is the solid-phase fraction and the vertical axis is the distance from the top of the sample. Initially, the lower zone of the image corresponds to 100% solid phase and the upper zone to 100% liquid phase. In the average diagram, the analyzed results of the solid- and liquid-phase zones do not show perfect 100% and 0% values, but this may be due to the influence of statistical errors and residual background components. However, as shown in the diagram, each zone shows moderately constant values and can be used to determine the solid- and liquid-phase zones. In addition, there is a zone of gradual change in phase fraction between these two zones, which is considered the zone where the solid-liquid interface moved within 30 min. This interfacial zone moves to the top over time, until eventually the whole area becomes solid.  
Figure 14: Results of solid-phase fraction imaging during the solidification. For each time period, the left figure shows the mapped real-space distribution of the solid-phase fraction and the right figure shows its horizontal average. On the right, the colored area indicates the location of the solid–liquid coexistence zone, while the green line indicates the interface location estimated by linear fitting where the solid-phase was 50%.  
Subsequently, the average solid-liquid interfaces were estimated by the position of the 50% solid-phase fraction for all analyzed images. The results are shown in Figure 15. The horizontal axis shows the time since the solidification process began, and the vertical axis shows the position from the top of the sample. The results are relatively consistent with the time dependence results of a previous study [26; 27] estimated from neutron transmission images. Based on the results, we estimated the solidification velocity during the experiment, and this is shown in Figure 16. The result of this study shows a tendency for the solidification velocity to gradually increase with time, which may be reasonable considering the decrease in the liquid-phase volume over time, i.e., the decrease in heat storage capacity.