# Space-Time Prediction of PM\({}_{2.5}\) Concentrations in Santiago de Chile Using LSTM Networks
###### Abstract
Several methods have been proposed in the literature for predicting the PM\({}_{2.5}\) concentrations; most of them are based on statistical models [6; 21; 22; 23] and neural networks [24; 25]. In general, the existing works for the prediction of PM\({}_{2.5}\) concentrations in Santiago de Chile using neural networks are based on temporal models [8; 14; 25; 26; 27]. The main difficulty in predicting space-time pollution is due to the fact that air pollutants are strictly correlated with meteorological variables (normally collected at the same spatial points and temporal lags) which are often not available when the prediction at new site has to be made. Additionally, the correlations of the pollutant concentrations with past meteorological variables are often weak, complex and show nonlinear behavior. For this reason, statistical spatio-temporal models which normally include linear relations with exogenous variables cannot be used if predictions or simulations of these variables are not provided (see, for example, [6; 28]). The long short term memory (LSTM) network proposed by [PERSON] and [PERSON] [29] is a recurrent neural network which is typically used for temporal predictions. However, this model has the limitation that it does not allow predictions to be made at points other than those available during training. Given that in Santiago de Chile, few monitoring stations are available in the town, a space-time approach is necessary to predict pollution at new locations where measurements are not available. The main aim of this work is considering predictions at spatial points other than those trained, by proposing a recurrent neural network that uses the historic information collected by monitoring stations located at some geographic points for predicting the pollution at new sites for \(n-\)ahead time steps. In particular, in this work we used the LSTM neural network [29] for the prediction of PM\({}_{2.5}\) concentrations in the city of Santiago de Chile, considering the measurements of multiple meteorological variables (such as speed and wind direction, temperature and relative humidity) and pollutants (nitrogen dioxide, PM\({}_{2.5}\) and PM\({}_{10}\)) collected in the previous 24 h. In other words, the proposed model can be used for forecasting the PM\({}_{2.5}\) levels at any spatial point by generating a space-time prediction using past information and spatial locations. The novelties of this work can be summarized in the following two points: (a) the proposal of a space-time machine learning model for predicting the pollution at arbitrary spatial points and at any future time; (b) the application to the pollution prediction in Santiago de Chile, one of the cities with the worst pollution in the world. About the point (a), the existing pollution prediction studies based on neural networks typically made temporal predictions for different spatial points, without considering spatial correlations, and other works used statistical space-time models where knowledge of future values of meteorological variables is assumed. These variables are normally predicted or simulated by complex deterministic models. In this proposal the prediction can be made at each point in the space without knowing the past values at the same point and without the need to run a different model for the prediction or simulation of the exogenous variables, since the past variables of meteorological data are considered as the input of the proposed model. About the point (b), few works have addressed space-time pollution prediction in Santiago de Chile, especially due to the poor availability of monitoring stations. We think that the proposed model could be used by the governmental decision makers for implementing temporary restriction measures in areas where there are not available data, and consequently reducing short term effects on human health due to PM\({}_{2.5}\) exposure.