# Space-Time Prediction of PM\({}_{2.5}\) Concentrations in Santiago de Chile Using LSTM Networks
## 6 Discussion  
When analyzing the results of the experiments considering the prediction for one hour in the future, it can be observed that the use of seven stations allowed us to obtain better predictions than considering eleven stations, which included the four furthest stations: Las Condes, Puente Alto, Quilicura and Talagante. We believe that this was due to the fact that the four outer stations observe values that have lower correlations with those of the seven closest stations. Therefore, this theoretically affects the quality of the short-term forecasts enough to reduce their quality. For example, regarding the \(R^{2}\) for Cerro Navia and Cerrillos, they decreased from 0.84 and 0.73 to 0.82 and 0.71, respectively, when considering the data from the 11 stations. We think that this may have been due to the presence of factors that could alter pollution, such as some particular sources of emissions (traffic, heating, factories, etc.) or particular meteorological conditions (temperature, wind, humidity, etc.). Remarkably, we observe that the 24 h forecasts did not differ majorly when considering seven and eleven stations. In particular, we observe that the best average values of \(R^{2}\) and MAE occurred when considering seven stations, though slightly, but the best RMSE occurred for 11 stations. We can suggest that there is no best configuration in this case, unlike the case of predicting one hour in the future. We think that this result is explained because when considering 24 h, it is possible that the use of more stations can influence the prediction. That is, the patterns of the remote stations may be more correlated when considering a longer horizon than just 1 h in the future. However, in practical terms, although there is no greater difference in performance, naturally a model that considers more stations appears to be more applicable. When comparing the results of predictions both 1 h ahead and 24 h ahead, it is evident that the results were much better for 1 hour ahead for all tested models. We believe there are two main reasons for this difference in performance. Firstly, when predicting 24 h simultaneously, the neural network generates a weight configuration that tries to respond to all the hours of the output variables simultaneously. In other words, learning seeks to adjust many outputs simultaneously, which may mean that performance must be reduced in one output variable to improve another. The second reason is that the prediction at a longer temporal distance is naturally more uncertain. This can be seen in Figure 7, where as the hour to be predicted moves further away from the input hours, the performance drops noticeably. The R\({}^{2}\) is greater than 0.7 in the first hour, and ends up less than 0.4 at hour 24. A possible solution is to make predictions for every hour in order to maximize the use of the neural network; however, this can be expensive. Another way would be to explore new neural architectures that better handle adaptation to different output variables. In relation to the pre-processing, the training process considered all the stations, though the information of the target station was canceled while maintaining its coordinates. In this way we hoped that the model would learn to use the other stations to predict a particular station, and thus we avoided typical temporal modeling. The use of all stations can be seen as similar to other PM\({}_{2.5}\) spatio-temporal prediction work [41], although they did not perform applied information override. An interesting alternative is to remove a training station while it is being used for testing. The problem that appears is that when training, it is necessary to eliminate the station associated with the output variable (in order to imitate the procedure in the testing process), for which the number of stations is reduced by one. In further experiments, we found that this reduction causes the performance of the tested network to drop.