## 5 Experimental Setup and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Learning Rate** & **Layers** & **L1** & **L2** & **L3** \\ \hline \multirow{2}{*}{0.0001} & 8 \(\times\)[30] & 0.1508 & 0.1604 & 0.1302 \\  & 8 \(\times\)[50] & 0.1077 & 0.17493 & 0.1193 \\ \hline \multirow{2}{*}{0.001} & 8 \(\times\)[30] & 0.05498 & 0.07536 & 0.05237 \\  & 8 \(\times\)[50] & 0.0849 & 0.1557 & 0.127 \\ \hline \multirow{2}{*}{0.01} & 8 \(\times\)[30] & 0.2984 & 0.3038 & 0.3044 \\  & 8 \(\times\)[50] & 0.2984 & 0.3038 & 0.3043 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Relative error of links for the fixed tanh activation function. the first, second, and third columns. The first, second, and third rows respectively represent the network's links, L1, L2, and L3, that show the promising results. The pointwise error of all three links and the loss convergence history are presented in Figures 8 and 9, respectively. Based on Figure 8, the dominant blue color indicates lower prediction error, which indicates the model effectively captures the general congestion pattern. It is evident from Figure 9 that even after 15,000 epochs, the loss for all three links remains continuously decreasing. Figure 6: (**a**) Predicted traffic speed of Link L1, (**b**) predicted traffic speed of Link L2; (**c**) predicted traffic speed of Link L3. Figure 7: Actual and predicted speed at three different times 125, 250, and 675 respectively given by the first, second, and third columns. The first, second, and third rows respectively represent the network’s links L1, L2, and L3. In our case, we use an adaptive activation function in accordance with [PERSON] et al. (2019). However, the adaptive activation function does not significantly improve the results. Figures 10 and 11 present representative results of the framework with adaptive activation. In Figure 11, the loss of links L1 and L2 does not diminish after about 50 epochs, despite a rapid convergence at the initial epochs. Although the proposed approach successfully captured the complex traffic behavior in the network, the model needs further improvements and fine tuning to eliminate the large errors. In addition, the lesser accuracy is likely due to ambiguities in the data collection process. For example, the assumption of constant traffic state across a cell may be reasonable  
Figure 11: Loss history of all three links for 500 epochs with adaptive activation function. Figure 8: Pointwise error of Links L1, L2, and L3. Figure 10: Actual and predicted speed at three different time intervals of Link L3 with adaptive activation function. Figure 9: Loss history over the number of epochs with fixed tanh activation function. from a macroscopic perspective, but it may not necessarily satisfy the partial differential equation that describes traffic flow. Moreover, the data failed to follow the basic flow conservation phenomenon at the intersecting points. We further compare the data and model predictions at the intersection using Figure 12.  
The larger error at the intersection points is due to discrepancies in the actual data. Since the data are estimated as described in the previous section and the data are not preprocessed to strictly satisfy the flow conservation at the intersection points. Figure 13 shows the flow conservation error1 and error2 at intersections 1 and 2, respectively. The flow conservation error in the observed data is due to the assumption of grid cells while estimating the traffic state variables from the trajectory data. The error could be reduced to zero by assuming a minimally small-sized cell. The time complexity of the algorithm to compute traffic state variables from the space-time diagram is \(O(n^{2})\), and a too small-sized cell could be computationally expensive. The flow conservation error distribution shows lesser violations at intersection 2 and that the prediction results are better as compared to intersection 1.