# Multi-Scale Temporal Convolutional Networks for Effluent COD Prediction in Industrial Wastewater
## 4 Results and Discussion
Different from the fixed receptive field utilized by CNN for capturing local characteristics, the causal convolution in TCN enables it to refer to the state of time \(t-1\) in the previous hidden layer when learning the changes at time \(t\). Thus, TCN can provide more accurate predictions for overall trends in the time series but is sometimes less effective than CNN on short-term abrupt changes, which can also be confirmed by comparing Figures 13a and 14a. Considering that the dilation rate allows TCN to adjust the size of its receptive field window and makes its learning range more flexible, TCN outperforms LSTM on the dataset, which contains many fluctuations only existing in a short period. RMSE of the TCN model on the test  
Figure 12: The forecasting results of the MSTCN model: (**a**) training set and (**b**) test set. Figure 13: Comparison of CNN and LSTM on the test set: (**a**) CNN and (**b**) LSTM. set is 0.5071, which is 10.14% lower than LSTM, while the \(R^{2}\) value is 4.72% higher. However, MSTCN still shows significant improvements over TCN in both training and test performance metrics, as the multi-scale approach of MSTCN enables the TCN layers in it to be trained separately to learn the unique temporal patterns of the target variable for each scale. Thus, there is a 7.59% increase in test \(R^{2}\) and a 22.56% decrease in \(RMSE\) compared with TCN. The attention mechanism is a method that can highlight important information by assigning higher weights to critical features in the input sequence [35]. By inserting an attention module between the LSTM and the input layer, the negative influence of redundant information on LSTM performance can be effectively reduced during the training process. Figure 14b plots the forecasting results of ALSTM on the test set, and it is obvious that there are smaller differences between the ALSTM curve and the observed one during the stage with a gradually increasing trend. Comparing Figures 14a and 14b, ALSTM has a superior explanation of dynamic changes at the end of the sequence than TCN. The test \(R^{2}\), \(RMSE\), and \(MAE\) of it are 0.8747, 0.4496, and 0.3552, indicating a second-ranked performance among all comparative models. Due to the GCN layers, MSTCN can extract more diverse feature representations with the extracted relationships at each scale from the adjacency matrix. As a result, these metrics of MSTCN are 3.39%, 12.64%, and 22.14% improved than those of ALSTM. Considering the convolution operations used in CNN, TCN, and MSTCN, their training time is much shorter than LSTM and ALSTM, which are based on serial computation. MSTCN takes 8 s to reach its optimal performance, which is 2.2 s shorter than ALSTM and 6.3 s shorter than LSTM. The ability of MSTCN to converge faster while maintaining high predictive performance suggests its scalability and applicability in complex and large-scale industrial settings [36]. Overall, the proposed MSTCN model shows high predictive accuracy in both training and test sets, making it a reliable tool for forecasting effluent COD concentrations after wastewater treatment. The model effectively identifies and simulates both long-term trends and short-term fluctuations, which is crucial for achieving accurate predictions from time series with complex data patterns [37]. These findings highlight the potential of MSTCN for improving accuracy and operational efficiency in wastewater quality prediction.