# Space-Time Prediction of PM\({}_{2.5}\) Concentrations in Santiago de Chile Using LSTM Networks
## 5 Experiments
### One-Hour-Ahead Forecasting  
We applied the different models to forecast the \(PM_{2.5}\) one hour ahead. This task is the prediction which had the highest expected certainty because there was less discontinuity with the historical data. We used two experiments: (i) first we considered the seven nearby stations, and then (ii) the eleven available stations. We complement these experiments by visually displaying the prediction results at a particular station. In this way we hope to see the effect of the more distant stations on the quality of the predictions. (i) Prediction considering the seven closest stations: In Table 7, each of the seven trained networks is displayed, where the column Station refers to the station to be predicted. In relation to metric \(R^{2}\), the results show that LSTM-4 obtained the best results in comparison to other alternative methods. In particular, the station Cerro Navia delivered the highest prediction quality of the PM\({}_{2.5}\) pollutant with \(R^{2}\) of 0.844, followed by Pudahuel, Cerrillos and El Bosque. On the other hand, the lowest quality of prediction was obtained on La Florida with an \(R^{2}\) of 0.679. On average, the prediction quality remained relatively high with a \(R^{2}\) of 0.741. We think that these good results are explained by these stations being close. Regarding RMSE and MAE, the results are similar to the \(R^{2}\) results: LSTM-4 was the best method again. LSTM obtained the best results for MAE. We also tested a simple baseline prediction based on the mean of the last value of PM\({}_{2.5}\); however, the results are poor: the average \(R^{2}\), RMSE and MAE were 0.002, 25.7 and 20.4. In general, we found that the methods based on recurrent neural networks perform better than simpler methods such as FFN or LR. (ii) Prediction considering all 11 stations: Table 8 displays the results for each of the 11 trained networks, where the Station column indicates the station to predict. When considering the metric \(R^{2}\), it appears again that the LSTM-4 algorithm obtained the highest value, it being very close to the one given by GRU. As in the previous experiment, the Cerro Navia station delivered the highest PM\({}_{2.5}\) forecast quality with a maximum \(R^{2}\) of 0.816 (LSTM-4), followed by Pudahuel (LSTM), Quilicura ( LSTM-4) and Cerrillos (GRU). On the other hand, the lowest prediction quality was obtained in the stations of Puente Alto and Las Condes with \(R^{2}\) of 0.461 and 0.489, when considering the LSTM-4 method. On average, the quality of the predictions was still relatively high, given an \(R^{2}\) of 0.657, although clearly lower than the result obtained using the seven nearby stations. We believe that this decrease in accuracy can be explained by the incorporation of very distant stations, which could have confused the neural network. Regarding RMSE, the results are similar to those of \(R^{2}\): the LSTM-4 algorithm was again the best method, closely followed by GRU. In MAE, the LSTM network obtained the best average result. Additionally, we also tested a simple benchmark prediction based on the mean of the last values of PM\({}_{2.5}\). In this case, the results were not good, given average \(R^{2}\), RMSE and MAE of -0.501, 22.3 and 13.77, respectively. We found that methods based on recurrent neural networks with multiple layers obtained the best performance on average.