## 4 Results  
The results provided in this paper were obtained operating on a computer with the following properties: memory of 15.5 GB, processor Intel Core i7-6500U CPU @ 2.50 GHz \(\times 4\), disk capacity of 512.1 GB with Ubuntu 20.04.1 LTS 64-bit OS. The algorithms are coded in Python 3.8 and the explained neural networks have been built and trained using the TensorFlow 2.3.0 library. Aiming to make a fair comparison, in terms of computational performance between the proposed reconstruction algorithm and the original implementation of LHCb in a local environment, a version of the original calorimeter reconstruction implemented in LHCb was replicated in Python with the same computational complexity, referred to as the Python version of LHCb algorithm. To make sure the comparison between both algorithms was fair, we defined a metric of efficiency on the reconstruction as relative error. This relative error calculated the difference of energy between reconstructed clusters and the true clusters reconstructed by the original LHCb reconstruction algorithm implemented in the LHCb framework. Using the relative error metric in the reconstructed clusters from the proposed deep learning algorithm gives as a result the first entry in Table 4. In the same table, we find the relative error for the reconstructed clusters obtained with the Python version of the LHCb algorithm. The values shown, concerning the two compared algorithms in relative error, were obtained as the mean values from over 200 simulation samples from the full LHCb calorimeter. It can be observed that the proposed deep learning approach shows, in general, a lower relative error value than the original version. Although this needs to be studied in detail with further experimentation, these results give us a hint that the two algorithms behave as expected and further comparisons will be fair. Figure 5: Detailed scheme of the proposed reconstruction dataflow for the inner calorimeter region. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Region** & **Image** & **Training** & **Neurons** & **Parameters** & **Training** & **RMSE** \\  & **Shape** & **Samples** & **Per Layer** & & **Time** & **RMSE** \\ \hline All & \(5\times 5\) & 270,000 & [64; 64; 32; 64] & 108,993 & 2130.4 s & 168.884 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter summary of the cluster and overlap neural network. Results, in terms of computational performance, are measured as the time in seconds elapsed between the reading of the readout cell values, and the generation of the list of clusters for the three regions of the calorimeter. The execution of both methods was done using a single thread in each case. Figure 6 shows a plot of the computational time for the number of energy cells (hits) on a single sample of a calorimeter simulation (event). The time plotted is measured as a mean of one hundred iterations on the same event for 200 different events. Looking at the curve from the Python version of the LHCb algorithm (iterative), it performs really fast in events with a low number of energy cells. However, it shows a clear quadratic growth with the number of cells activated. On the other hand, the deep learning approach (DL total) shows nearly constant behavior towards the number of cells. Although it has a small positive slope of \(4.97\times 10^{-6}\), the tendency shows to be linear. Even so, around 72% of the events processed in the testing have less than 2575 energy cells and, therefore, stay under the time performance curve of the deep learning approach. Even so, we achieved a constant computational time with independence of the event complexity. In addition, as stated in Section 3.2, for the first step of the proposed reconstruction process, the information from the three regions of the calorimeter needs to be treated separately. Given that the reconstruction process is the same for each region, excepting the ad-hoc local maxima neural network, another way of accelerating the execution time is executing the reconstruction of the three regions in parallel.