# Space-Time Prediction of PM\({}_{2.5}\) Concentrations in Santiago de Chile Using LSTM Networks
## 5 Experiments
### 24-h-Ahead Forecasting
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Station** & **Metric** & **LR** & **FFN** & **LSTM** & **GRU** & **LSTM-4** \\ \hline \multirow{4}{*}{Cerrillos} & R2 & 0.343 & 0.375 & 0.383 & 0.392 & **0.393** \\ \cline{2-7}  & RMSE & 15.89 & 15.50 & 15.40 & 15.29 & **15.27** \\ \cline{2-7}  & MAE & 7.66 & 7.20 & 6.51 & **6.46** & **6.46** \\ \hline \multirow{4}{*}{Cerro Navia} & R2 & 0.364 & 0.384 & **0.450** & 0.449 & 0.445 \\ \cline{2-7}  & RMSE & 20.04 & 19.73 & **18.64** & 18.67 & 18.73 \\ \cline{2-7}  & MAE & 8.77 & 8.17 & 6.71 & **5.98** & 6.13 \\ \hline \multirow{4}{*}{El Bosque} & R2 & \(-\)0.268 & 0.394 & 0.417 & **0.422** & 0.416 \\ \cline{2-7}  & RMSE & 25.36 & 17.54 & 17.19 & **17.12** & 17.22 \\ \cline{2-7}  & MAE & 15.45 & _7.97_ & 7.63 & **7.29** & 7.47 \\ \hline \multirow{4}{*}{Independen.} & R2 & \(-\)1.220 & 0.371 & 0.386 & **0.402** & 0.401 \\ \cline{2-7}  & RMSE & 21.85 & 11.62 & 11.49 & **11.34** & **11.34** \\ \cline{2-7}  & MAE & 13.64 & 6.23 & **5.99** & 6.16 & 6.08 \\ \hline \multirow{4}{*}{La Florida} & R2 & \(-\)0.862 & 0.352 & 0.379 & **0.425** & 0.386 \\ \cline{2-7}  & RMSE & 23.20 & 13.69 & 13.40 & **12.90** & 13.33 \\ \cline{2-7}  & MAE & 14.93 & 6.98 & **6.52** & 6.60 & 6.53 \\ \hline \multirow{4}{*}{Las Condes} & R2 & \(-\)2.686 & \(-\)0.351 & \(-\)0.137 & **0.292** & 0.248 \\ \cline{2-7}  & RMSE & 24.21 & 14.66 & 13.45 & **10.62** & 10.94 \\ \cline{2-7}  & MAE & 15.65 & 7.81 & 6.72 & **5.87** & 5.91 \\ \hline \multirow{4}{*}{POHiggins} & R2 & \(-\)0.634 & 0.374 & 0.387 & 0.383 & **0.392** \\ \cline{2-7}  & RMSE & 22.88 & 14.15 & 14.01 & 14.05 & **13.95** \\ \cline{2-7}  & MAE & 14.61 & 7.19 & 6.89 & **6.57** & **6.57** \\ \hline \multirow{4}{*}{Pudahuel} & R2 & 0.348 & 0.375 & 0.407 & **0.410** & 0.404 \\ \cline{2-7}  & RMSE & 17.85 & 17.48 & 17.01 & **16.98** & 17.06 \\ \cline{2-7}  & MAE & 7.08 & 6.95 & 6.67 & **6.28** & 6.54 \\ \hline \multirow{4}{*}{Puente Alto} & R2 & \(-\)0.434 & 0.108 & 0.112 & **0.185** & 0.160 \\ \cline{2-7}  & RMSE & 27.75 & 21.89 & 21.83 & **20.92** & 21.24 \\ \cline{2-7}  & MAE & 16.92 & 10.74 & 10.61 & 10.53 & **10.47** \\ \hline \multirow{4}{*}{Quilicura} & R2 & \(-\)0.747 & 0.404 & 0.424 & 0.428 & **0.439** \\ \cline{2-7}  & RMSE & 22.62 & 13.21 & 12.99 & 12.94 & **12.81** \\ \cline{2-7}  & MAE & 14.29 & 6.60 & 5.94 & **5.93** & 6.03 \\ \hline \multirow{4}{*}{Talagante} & R2 & \(-\)0.672 & 0.294 & 0.333 & **0.367** & 0.339 \\ \cline{2-7}  & RMSE & 22.98 & 14.93 & 14.51 & **14.13** & 14.44 \\ \cline{2-7}  & MAE & 14.27 & 7.39 & **6.08** & 6.11 & 6.38 \\ \hline \multirow{4}{*}{Average} & R2 & \(-\)0.588 & 0.280 & 0.322 & **0.378** & 0.366 \\ \cline{2-7}  & RMSE & 22.24 & 15.85 & 15.45 & **15.00** & 15.12 \\ \cline{2-7}  & MAE & 13.03 & 7.57 & 6.93 & **6.71** & 6.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Metrics of space-time prediction considering 11 stations, of 24 h in the future. Bold font indicates best results. In Figure 7 we visually analyze the results of \(R^{2}\) for each of the 24 h at Cerro Navia station. It can be seen that the recurrent networks have high values of \(R^{2}\) for the first hour (0.71), and then they steadily decay. Around hour 12, the value of the metric slowly decays. This is explained by the greater uncertainty due to the accumulated time. The same behavior is evident for the simpler methods, such as FFN and LR, those their results are generally much lower in quality compared to those of the recurrent networks. This behavior was repeated for the other stations and in the other metrics; the global metrics must be carefully analyzed. In Figure 8 we visually analyze the 24 h forecasts for 1 July 2013 at the Cerro Navia station. It can be seen that the LSTM-4 model managed to predict PM\({}_{2.5}\) values quite well; however, for the afternoon it tended to be imprecise. This behavior was expected due to the greater uncertainty in hours far from those of the training set.