# Space-Time Prediction of PM\({}_{2.5}\) Concentrations in Santiago de Chile Using LSTM Networks
## 5 Experiments
### 24-h-Ahead Forecasting  
In this experiment we performed space-time prediction of 24 h in the future. This problem is more difficult than the 1 h prediction because there were more variables to adjust simultaneously, which was verified in the results. In this case, we again performed two experiments, as in the previous Section: (i) we first evaluated the seven nearby stations, and then (ii) the eleven available stations. We also complement these experiments by visually displaying the results of the evolution of R\({}^{2}\) and the 24 h predictions at a particular station. (i) Prediction considering the seven closest stations: Table 9 presents the results considering all the techniques proposed for the 24 h prediction. The results of the \(R^{2}\) metric show that the LSTM-4 neural network obtained the best results, closely followed by the GRU network. As when predicting 1 h ahead, the Cerro Navia station provided the highest PM\({}_{2.5}\) prediction quality, with an \(R^{2}\) of 0.411 using the LSTM method, followed by El Bosque (LSTM) and Cerrillos (LSTM-4), which provided values higher than 0.4. On the other hand, the lowest prediction quality was obtained in Florida, with an \(R^{2}\) of 0.330. On average, the quality of the prediction was relatively low, with a \(R^{2}\) of 0.38. Note that this \(R^{2}\) corresponds to the mean of 24 values of \(R^{2}\), one for each hour. The values for the first hour were much better than for hours 12 or 24. For example, in Cerro Navia, the \(R^{2}\) was 0.62 for hour 1 and 0.37 for hour 24. Regarding RMSE and MAE, the results are similar for \(R^{2}\): the LSTM-4 algorithm appears to been the method with the best results, being closely followed by GRU. Again, we tested a simple prediction based on the mean of the last 24 PM\({}_{2.5}\) values for all training stations. The results were very poor, being on average \(-0.588\), 24.4 and 18.8 for the \(R^{2}\), RMSE and MAE, respectively. In summary, the methods based on recurrent networks appear to be the ones with the best performances. Figure 6: Comparison of real and one-hour-ahead values of PM\({}_{2.5}\) at the Cerro Navia station during 9 August 2013. (ii) Prediction considering 11 stations: Table 10 shows the results all the methods for 24 h predictions. In relation to metric \(R^{2}\), in this case the neural network GRU obtained the best results. In particular, Cerro Navia delivered the highest prediction quality of the PM\({}_{2.5}\) pollutant with an \(R^{2}\) of 0.45, followed by Quilicura, Pudahuel, and El Bosque. On the other hand, the lowest-quality predictions were obtained for Las Condes, with an \(R^{2}\) of 0.292. On average, the prediction quality remained relatively low with an average \(R^{2}\) of 0.38. We note that this \(R^{2}\) corresponds to the average of 24 \(R^{2}\), one for each hour. The values for the first hour are much better than for the 12 th or 24 th hours. For example, for Cerro Navia, the \(R^{2}\) was 0.74 for hour 1 and 0.35 for hour 24. This behavior was repeated for all stations. In subsequent analysis, we will focus on this point for one station. Regarding RMSE and MAE, the results are similar to those of \(R^{2}\): the GRU algorithm was the best method again. We also tested a simple baseline prediction based on the mean of the last 24 values of PM\({}_{2.5}\) for all training stations. In this case, the results were very poor; the average \(R^{2}\), RMSE and MAE were \(-1.12\), 40.3 and 18.2. Similarly to the previous experiment, we found that the methods based on recurrent neural networks preformed better than simpler methods, such as FFN and LR.