# Space-Time Prediction of PM\({}_{2.5}\) Concentrations in Santiago de Chile Using LSTM Networks
## 2 Related Works  
Spatio-temporal prediction is a challenging issue, given that spatial and temporal correlations of data have to be detected simultaneously. Many statistical and computational models have been proposed for dvarious fields, including crime, traffic and transportation, climate and environment monitoring, hydrology and epidemiology [30]. Most of the literature on spatio-temporal models presents statistical approaches based on separable or no separable spatial and temporal covariance structures. An extensive review of geostatistical space-time models for addressing environmental problems (monitoring acid deposition, forecasting precipitation, pollution, etc.) is presented in [31]. Hierarchical spatio-temporal modeling concepts and computational methods are described in [32], considering many issues, including environmental processes and climate trends, besides mapping public-health data and the spread of invasive species. Recently, especially due to the availability of big datasets, computational models based on deep neural networks have arisen for predicting space-time data. [PERSON] et al. [33] introduced a new framework for the spatio-temporal prediction of climate and environmental data by decomposing time series into a basis function and stochastic spatial coefficients. In [34], deep learning (DL), and in particular, recurrent neural networks (RNNs), were implemented for wind speed forecasting, motivated by the use of renewable energy in northeast of the U.S. [PERSON] et al. [35] proposed two adaptive modules for enhancing the graph convolutional network (GCN) for understanding traffic dynamics and predicting the future status of an evolving traffic system. A slightly different approach consists of splitting the whole dataset into several subsets in a hierarchical manner and training a local prediction model for each subset, as in [PERSON] et al. [36], or considering a decomposition of the original series, as proposed by [PERSON] et al. [37]. Regarding the prediction of PM\({}_{2.5}\) concentrations in Santiago de Chile, various models have been proposed based on statistical methods or classical neural networks [6; 8; 26]. [PERSON] et al. [6] proposed an improved Bayesian spatio-temporal dynamic model for the prediction of PM\({}_{2.5}\) in the city of Santiago de Chile by calibrating meteorological variables derived from the Weather Research and Forecasting Model (WRF). From a neural-network perspective, [PERSON] et al. [26] used an approach based on multiperceptron neural networks, subsequently improving the quality of the model by considering meteorological variables such as wind direction [8]. In southern Chile, [PERSON] et al. [27] proposed a pollution prediction model based on a mixture of neural networks and ARIMA models. Regarding the pollution study in other countries, [PERSON] et al. [38] considered the use of various stacked models of LSTM recurrent networks and multilayer perceptrons for the prediction of pollution in North China, obtaining that the use of LSTM networks allowsbetter performance. [PERSON] and [PERSON] [39] proposed a mixed model consisting of a sequence starting with a convolutional network whose output feeds a recurrent short-long memory (LSTM) network for PM\({}_{2.5}\) concentration prediction in Beijing and Shanghai. It achieved an average of 97.8% correct prediction. [PERSON] et al. [40] used satellite imagery combined with ground-level measurements and deep convolutional neural networks, achieving a value of 0.75 for \(R^{2}\). [PERSON] et al. [41] combined convolutional networks with recurrent networks, thereby achieving a mean square error value of 0.72 for the next 72 h in the Jing-Jin-Ji area, Beijing. [PERSON] et al. [42] was able to forecast the concentrations of PM\({}_{2.5}\) and PM\({}_{10}\) for the city of Bogota (Colombia). They performed principal component analysis for the development of forecast models and artificial neural network and clustering methods.