## 3 Results
Therefore, the given table shows only testing's dataset performance. This average performance for each metric is in Figure 6. A single plot could plot both metrics, as their domains are the same when considering the absolute value of \(r\), as \(-1\leq r\leq 1\) and \(R^{2}\leq 1\), but \(0\leq|r|\leq 1\), thereby not showing if the Pearson correlation is positive or negative, but only measuring how strongly correlated are both sets of data. There is a vertical division on the plot: by the sampling method, then by the type of dataset, and finally by the loss function used. Moreover, the color represents the type of layer, and the type of dot the metric (\(|r|\), \(R^{2}\)). If both metrics are at maximum, the model would achieve the best performance, as higher is better for both metrics. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Metric**} & \multirow{2}{*}{**Layer**} & \multirow{2}{*}{\(\mathbf{L}\big{(}\hat{y},y\big{)}\)} & \multicolumn{4}{c}{**Up-Sampling**} & \multicolumn{4}{c}{**Down-Sampling**} \\  & & & \(F_{x}\) & \(F_{y}\) & \(F_{z}\) & **Avg** & \(F_{x}\) & \(F_{y}\) & \(F_{z}\) & **Avg** \\ \hline \multirow{8}{*}{\(R^{2}\)} & \multirow{4}{*}{GRU} & MAE & 0.76 & 0.96 & 0.1 & 0.6 & 0.64 & 0.96 & 0.09 & 0.56 \\  & & MSE & 0.77 & 0.96 & 0.17 & 0.63 & 0.75 & 0.95 & 0.06 & 0.58 \\  & & MSLE & 0.78 & 0.9 & 0. As shown in Figure 6, the best \(|r|\) performance was achieved using up-sampling (right side) on the validation dataset, via LSTM, which also had the best \(R^{2}\)'s performance and MSE. However, performance should be evaluated on the data unknown to the model, the testing dataset, as that reassembles a real-life situation. When considering only the testing dataset, the LSTM layer delivered the best performance, using the up-sampling method and MSE loss function, by both \(|r|\) and \(R^{2}\) performance metrics. Even though the performance was better using the up-sampling method, models trained using up-sampled data took double the time used for training using down-sampled data. Considering the time factor, differences in metrics on the testing dataset are not extensive, considering the best performance delivered by LSTM and MSE. Overall, the type of layer seems to be a determinant factor in model performance: LSTM showed the best performance in both metrics, with all combinations of loss functions and sampling methods; followed by GRU with medium performance in most cases, with a few exceptions in which the Simple layer performed better, such as on the validation dataset using MAE as the loss function; and finally, the Simple layer, which not only took longer for training, but also performed worst when compared to the other types of layers. Moving on to loss functions, MSE performed best, and both MAE and MSLE decreased the  
Figure 6: Models’ performances considering Pearson’ \(|r|\) and \(R^{2}\) performance metrics. Models were created by changing a set of parameters: sampling method used for data (Up, Down), loss function (MAE, MSE, MSLE), and type of layer (GRU, LSTM, Simple). They were evaluated on several datasets (training, validation, testing) and performance was averaged for the three force dimensions (\(F_{x}\), \(F_{y}\), \(F_{z}\)) into a single metric (Avg). Each type of marker represents a performance metric (circle, triangle), and color represents the type of layer used (red, green, blue). The x-axis shows the combinations of loss functions, datasets, and sampling techniques; thus, the combination of marker and color reflects the performance of a given model in the y-axis. In this case, the combination with the highest \(R^{2}\) on the testing dataset was (up-sampling, MSE, LSTM), which is the same combination that had the best \(|r|\), as shown in Table 4.  
model's performance depending on the dataset, type of layer, and sampling method, as MSLE with Simple on the testing dataset performed best when using down-sampled data, whereas the same combination performed worst using up-sampled data.