## 2 Materials and Methods
### Dataset Description  
For this investigation, the publicly available dataset from Kaggle [12] was used. The dataset was provided by the team from the University of Minnesota, and their research [13] was also focused on addressing the problem of accurately reconstructing the locations of interactions in the SuperCDMS detectors using machine learning methods. In [13], the prototype SuperCDMS germanium detector was tested with a radioactive source positioned on a movable stage that can perform scanning from the center of the detector up to the near edge. The SuperCDMS germanium detector is a disk-shaped object that is 10 cm in diameter and 3 cm in height, with phonon sensors placed on the top and bottom surfaces to detect particles from a radioactive source. The sensors were used to measure phonons, i.e., quantized vibrations of the crystal lattice, which are produced from interacting particles and travel from the interaction location to the sensors. The number of phonons and relative arrival time to the particular sensors depends on the interaction and the sensor positions. The output of each sensor channel is a waveform for every interaction. In this experiment, the sensors were grouped into six regions labeled A, B, C, D, E, and F on both sides of the detector, as shown in Figure 1.  
To produce interactions at 13 different locations on the detector along a radial path from the center up to the detector's outer edge, a movable radioactive source was used. The 13 different locations are shown in Figure 2, while the numeric values of the locations are listed in Table 1.  
Figure 1: The detector regions of the SuperCDMS detector. The entire dataset consisted of 21 parameters and 7151 samples. However, the first parameter row number (\"Row\") was omitted from this research. The dataset was obtained by extracting a set of parameters for each interaction from the signals of five sensors. The extracted parameters are sensitive to interaction location, relative timing between pulses in different channels, and features of the pulse shape. The relative amplitudes are also relevant, but were not included in the dataset due to amplification instabilities in the experiment. For each interaction, the following parameters were recorded:  
* B, C, D, and F start--the time at which the signal pulse rises to 20% of the signal peak to Channel A. The variables in the original dataset are labeled as PBstart, PCstart, PDstart, and PDstart, respectively. * A, B, C, D, and F rise--the time required for the signal to rise from 20 % to 80% of its peak. These variables in the original dataset are labeled as PArise, PBrise, PCrise, PDrise, and PFrise,
* A, B, C, D, and F width--the width of the pulse at 80% of the pulse height. The height was measured in seconds. These variables in the original dataset are labeled as PAwidth, PBwidth, PCwidth, PDwidth, and PFwidth. * A, B, C, D, and F fall--the time required for a pulse to fall from 40% to 20 % of its peak. These variables in the original dataset are labeled as PAfall, PBfall, PCfall, PDfall, and PFfall. As seen from the minimum and maximum values shown in Table 2, all the input variables labeled \(X_{0}\) to \(X_{18}\) are all very small values in the \(10^{-6}\) to \(10^{-4}\) range. The target (output) variable, which is \(y\), is in the \(-41.9\) to 0 range. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Location** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** \\ \hline Coordinate x & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Coordinate y & 0 & \(-3.96\) & \(-9.98\) & \(-12.502\) & \(-17.992\) & \(-19.7\) & \(-21.034\) & \(-24.077\) & \(-29.5\) & \(-36.116\) & \(-39.4\) & \(-41.01\) & \(-41.9\) \\ \hline \end{tabular}
\end{table} 
Table 1: The measured coordinates of the interaction locations shown in Figure 2.  
Figure 2: Top view showing detector regions (A, B, C, D, E, and F) and interaction locations indicated with the “x” symbol in orange color.