## 3 Results
It is noticeable in Table 3 that layer type is a determinant factor for the \(t_{epoch}\), as the Simple layer took 76, 66, and 73 s with the up-sampling method, which contrasts greatly with LSTM's times (31, 30, and 33 s), and GRU's times (33, 30, and 32 s), so, at first glance, it seems that the Simple layer is less efficient than LSTM and GRU layers. It is worth noting that the more data, the greater the \(t_{epoch}\) would be as more data are processed; this is represented in each combination, as down-sampling times mostly are half of the up-sampling times because the up-sampling, in this case, was conserving the 9000 samples, whereas down-sampling was dropping even samples to reduce the number to 4500 samples. This phenomenon is represented in Simple's down-sampling \(t_{epoch}\) (32, 40, 32) when compared with up-sampling \(t_{epoch}\) (76, 66, 73). This can also be seen in the GRU layer down-sampling \(t_{epoch}\) (16, 17, 33) when compared with its up-sampling \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Layer**} & \multirow{2}{*}{**Sampling**} & **Loss Function** & \(t_{epoch}\) & \(t_{elapsed}\) & \(t_{elapsed}\) \\  & & \(L(\hat{y},y)\) & **(s)** & **(s)** & **(min)** \\ \hline \multirow{4}{*}{LSTM} & \multirow{4}{*}{Up} & MAE & 31 & 775 & 12.92 \\  & & MSE & 30 & 750 & 12.5 \\  & & MSLE & 33 & 825 & 13.75 \\ \cline{2-6}  & & MAE & 19 & 425 & 7.08 \\  & & MSE & 19 & 475 & 7.92 \\  & & MSLE & 15 & 375 & 6.25 \\ \hline \multirow{4}{*}{GRU} & \multirow{4}{*}{Up} & MAE & 33 & 825 & 13.75 \\  & & MSE & 30 & 750 & 12.5 \\  & & MSLE & 32 & 800 & 13.34 \\ \cline{2-6}  & & MAE & 16 & 400 & 6.67 \\  & & MSE & 17 & 425 & 7.08 \\  & & MSLE & **13** & **325** & **5.42** \\ \hline \multirow{4}{*}{Simple} & \multirow{4}{*}{Up} & MAE & 76 & 1900 & 31.67 \\  & & MSE & 66 & 1650 & 27.5 \\ \cline{1-1}  & & MSLE & 73 & 1825 & 30.42 \\ \cline{1-1} \cline{2-6}  & & MAE & 32 & 800 & 13.34 \\ \cline{1-1}  & & MSE & 40 & 1000 & 16.67 \\ \cline{1-1}  & & MSLE & 32 & 800 & 13.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean training time per epoch (\(t_{epoch}\)), for each combination of layer type, sampling method, and loss function. Total training time elapsed (\(t_{elapsed}\)) was also calculated as shown in Equation (14), considering \(n_{epochs}=25\) and using a GeForce GTX 1060 6 GB with NVIDIA Compute Unified Device Architecture (CUDA) ©Deep Neural Network library (cuDNN). Best times are in bold, which depend on average \(t_{epoch}=13\) when using (GRU, down-sampling, MSLE). (33, 30, 32). On the other hand, the loss function seems not to have a significant role in changing the \(t_{epoch}\), although in some cases of down-sampling using MSLE, \(t_{epoch}\) seems to be less in LSTM and GRU layers (\(\approx\)4 s) when comparing (19 s, 19 s) with 15 s in the case of LSTM, and (16 s, 17 s) with 13 s in the case of GRU. Moving on to prediction performance, two metrics were used: the Pearson correlation coefficient (\(r\)), shown in Equation (7), and the coefficient of determination (\(R^{2}\)), shown in Equation (4). The models used the following set of parameters: sampling method (up-sampling, down-sampling); type of layer (GRU, LSTM, Simple); loss function (MAE, MSE, MSLE); in addition, performance metrics obtained based on training, validation, and testing datasets--for the force on every axis (\(F_{x}\), \(F_{y}\), \(F_{z}\)), an additional average performance metric was calculated using all forces (Avg). Based on the trained RNN's performance, the coefficient of determination (\(R^{2}\)) was used as a performance metric to measure a model's performance (higher is better). Results are in Table 4, divided by the type of performance metric (\(R^{2}\), \(|r|\)) and sampling technique applied to the data (up-sampling, down-sampling). In ML, testing the dataset's performance is usually considered the most valid result because it reassembles a real-world scenario where the model would not have access to the new data beforehand.