## 3 Results
### Ground Truth 1
#### 3.1.4 Conv2D  
In Figure 11, R\({}^{2}\)-strength rankings for Conv2D with two time series are shown. Given that for Conv2D, adding a third time series did not work out well, only rankings per predictor pair could be obtained. When R\({}^{2}\)-strength is shown in the upper two panels of Figure 11, it means that the current time series pair is a significant contributor. Significance weights, which denote significant contributions of one time series to a target time series (instead of R\({}^{2}\) scores denoting a connection between a certain pair of predicting time series and one target time series), are reported between brackets. They were obtained as described in Section 2.2.3 and were considered significant if the cutoff of 0.70 was not exceeded. The lower two panels show a ranking (with 1 being the most active connection and 4 the least active connection).  
Figure 10: LSTM-NUE, Neural-Network Granger Scores rankings (Top) versus Truth 1 (Bottom), excluding self-connectivity. Color coding: dark green > light green > yellow > orange > red. The columns represent the targets, the rows the time series used for prediction.  
It can be seen from Figure 11 that, in the prediction of Target X1, out of three direct connections, only one is not significant (i.e., X2, X3 \(\rightarrow\) X1, Top-row), but this is only the case when Target X1 is not included as a predictor. Regarding an overall ranking (Ground Truth 1, Bottom-Left), it can be seen that X3 has the strongest self-connectivity, while for X1 and X2, self-connectivity is almost the same. This is observed in our results as well (R\({}^{2}\) = 0.36, 0.35 in both dipole conditions). Moreover, the obtained R\({}^{2}\) strength scores are not, or barely, dependent on the dipole condition. Next, while inspecting these results column-wise (hence, target-wise), a stronger connection between predictors X1, X2 and Target X1 than between predictors X1, X3 and target X1 were expected. However, these connections are quite similar (R\({}^{2}\) = 0.35 versus R\({}^{2}\) = 0.34 in the Far-Superficial condition, R\({}^{2}\) = 0.36 versus R\({}^{2}\) = 0.34 in the Far-Deep condition). While predicting target X2 using X1, X3, a significant, correct contribution from X1 to X2 is found (significance weight = 0.232, 0.120, Far-Superficial and Far-Deep condition, respectively), as well as a correct contribution from X3 to X2 (significance weight = 0.001, 0.048, Far-Superficial and Far-Deep condition, respectively). However, connectivity strength R\({}^{2}\) is very low (R\({}^{2}\) = 0.02 in both dipole conditions) in comparison with the situation in which target X2 is included in the predictor pair and in which case X3 is also considered a significant contributor (predictor pair = X2, X3, R\({}^{2}\) = 0.36,0.36, significance weights = 0.341,0.210 for X3, Far-Superficial and Far-Deep condition, respectively). The ranking for Target X2 is correct, as was the ranking for X1. Finally, we expected similar rankings for X2; X3 predicting X3 as for X1; X3 predicting X3 since neither X1 nor X2 contribute to X3. This is indeed the case for both conditions. As expected, significance weights for individual contributions of X1 and X2 to X3 were not significant (significance weights >0.70 in both dipole conditions).  
Figure 11: Conv2D, R\({}^{2}\)-strength score for time series pairs (Top) versus ranking of connections in the Ground Truth 1 (Bottom, 1 being the strongest), including self-connectivity. Color coding: dark green > light green > yellow > orange > red. The columns represent the targets, the rows the time series pairs used for predicting the target time series.