## 4 Discussion  
In this paper, a set of architectures of multilayer neural networks based on GRU, LSTM, and temporal convolution is proposed and considered. The implementation of the RFF and FRF architectures improves the results compared to [24]. The further modification of those architectures using bidirectional processing led to a 2-fold improvement in the forecast accuracy. The greatest improvement in accuracy of the forecast was achieved with the employment of a bidirectional temporal convolutional network architecture, though its initial variant provides results at a level comparable to traditional methods. Its bidirectional enhancement allows one to increase the accuracy of the forecast by 5-10 times. The observed dependence of the results on solar activity, a combination of indices, and the latitude shows that to determine the best method in each region, it is necessary to examine not only a set of architectures but also indices, as evidenced by the example with the Vsw index. It is important to note that the number of cells in bidirectional layers is two times higher than in unidirectional ones, but at the same time, a twofold increase in the number of cells in unidirectional networks did not lead to an increase in prediction accuracy but, on the contrary, reduced it. This result is due to overfitting. The bidirectional neural network includes two separate backpropagation passes: one is for the forward direction of inputs, and the second one is for the reverse direction. During the forward pass, the forward layer processes the input sequence in the original input direction and makes predictions for the output sequence. The backward layer processes the input sequence in reverse order during the backward pass and predicts the output sequence. When both passes are completed, their predictions are compared to the target output sequences and the error is propagated back to each respective layer through the network to update the weights. The forward and backward layer weights are updated based on the errors computed during the forward and backward passes, respectively. This process allows you to optimize the weights on a double amount of data--the original inputs and reverse inputs. For each of the layers of a bidirectional network, optimization is carried out on its own subspace of parameters. As for the comparison with the results of other works, as noted in the introduction, in many works, only MAE and RSME are mentioned as statistical characteristics, but MAPE is not indicated. The results obtained show that this is not sufficient. This is especially evident from the results for the Nicosia station, which has the highest TEC values. This can be demonstrated by the example of [23], where RMSE \(\sim\)0.5 TECU were obtained without specifying MAPEs. In this work, even smaller RMSE values were obtained regardless of latitude, indicating that the capabilities of the LSTM, GRU, and TCN methods for TEC prediction have not been exhausted. Apart from the differences in accuracy, it is important to note that significant discrepancies between the architectures in terms of computational costs are also observed. For bidirectional architectures, the computational costs are significantly higher than for unidirectional ones. In particular, among unidirectional architectures, for the FRF line of architectures, the training time was about 11 s, for the RFF line, the training time was about 9 s, and for the TCN, it was 2 s on average. The difference between the LSTM and GRU variants did not exceed 2 s on average, and the GRU-based architectures were converging at a higher rate. With the transition to bidirectional architectures, the training time for FRF and RFF architectures increased by more than 2 times and amounted to 27 and 22 s on average. For BiTCN, the training time increased to 4 s. The training was performed using a single RTX4080 and AMD Ryzen 9 7900X.