Urbanization trends worldwide show a clear preference for motorized road mobility, which has led to a degradation of air quality in recent years. Modelling and forecasting ambient air pollution is a relevant problem because it helps decision-makers and urban city planners understand this phenomenon, which is a signi cant threat to citizens' health. Generally, datadriven models su er from a lack of data. This article addresses the issue of having limited access to road tra c density and pollution concentration data by applying deep generative models, speci cally, Conditional Generative Adversarial Networks (CGAN). The main idea is to train CGANs to generate synthetic nitrogen dioxide concentration values given the road tra c density. The experimental data analysis from Montevideo (Uruguay) shows that the proposed method generates realistic (accurate and diverse) pollution data while using reduced computational resources.
The growth of the cities that prioritized motorized mobility (use of the individual or collective
vehicles) is having an undesired negative e ect on the dwellers' safety and quality of life.
A signi cant concern is the high generation of emissions (air pollutants) due to the rapid
development of car-oriented cities. Air pollution is a major concern because it has a negative
impact on the citizens' health, e.g., it provokes several respiratory diseases and it reduces life
expectancy [
One of the most important sources of air pollutants in urban areas is road mobility [
Arti cial Neural Networks (ANN) and Deep Learning (DL) are successfully applied to deal
with air outdoor pollution modelling, prediction, and forecasting, as data-driven methods [
This article focuses on training generative models, as a data augmentation approach, to
produce new information units (levels of NO2) to feed data-driven ANN methods for modelling,
forecasting, and predicting outdoor pollution. Generative Adversarial Networks (GANs) are
successfully used to train generative models [
GANs consist of two arti cial neural networks, a generator and a discriminator, that apply
adversarial learning. The generator is trained to deceive the discriminator by generating
\fake" or \arti cial" data samples transforming its inputs from a random latent space. The
discriminator learns how to distinguish between the \real" and \arti cial" data samples. GAN
training is formulated as a minimax optimization problem by the de nitions of generator and
discriminator loss [
The general training of a CGAN is graphically described in Figure 1.
The proposed approach applies a CGAN to train a generative model to get spatial pollution data. The CGAN learns the probability distributions of the generated pollutant given the road tra c density (given by a class from 1 to 5, from lowest to highest). Thus, the generative model has the road tra c density class as an input and returns the predicted NO2 concentration, which is a random value drawn from the probability distribution learned by the generator.
As the CGAN training is de ned as minimax optimization between the generator and the discriminator, the training process may oscillate without converging to an equilibrium. Thus, our method tracks the accuracy of the generator after each training epoch in terms of distance between the real and the generated distributions, and keeps a copy of the best generator found.
This section summarizes the main details of the methodology for training CGANs to create synthetic pollution data.
The training dataset studied here is provided by the open data portal o ered by the National
Government of Uruguay [
The road tra c density is classi ed in ve classes: A, B, C, D, and E, which represent densities from very low to very high. Table 1 and Figure 2 summarizes the distributions of data used as training dataset. As can be seen, the NO2 concentration increases with the road tra c volume. The classes are highly unbalanced (see Table 1), i.e., A class has 1280 (the maximum) and C class has 539 samples (the minimum). We randomly sampled over the classes for our experiments to select 539 samples of each class to balance the dataset to avoid training biases. Thus, the nal training dataset size is 2695 (539 5).
tra c density class mediean number of samples
In our research, both ANNs, the generator and the discriminator, are implemented as multilayer
perceptrons (MLP) [
For all the CGANs evaluated, the generators' input layer has size 65 (64 for reading the random latent space and one for the road tra c density label). The output layer has size one (for the predicted NO2 concentration). The input layer of the discriminator has size two (one for the road tra c density label and one for the NO2 concentration), and the output layer has size one (for the predicted label, i.e., fake or real ).
The main goal of the experimental evaluation is to analyze the impact on the training, the quality of the results, and the computational cost of the di erent CGAN architectures.
The performance is evaluated according to the loss values computed for the generator and
the discriminator during the training process. In this research, the function applied to compute
the loss is the binary cross-entropy (BCE) [
1 Ld = 2 Ex;y Pdata(x;y)[log(Dd(x; y))] 1 2 Ez Pz(z);y Py(y)[log(1
Dd(Gg(z; y); y))] ; Lg = Ez Pz(z);y Py(y)[log(1
Dd(Gg(z; y); y))] (1) (2)
In order to assess the quality of the generated samples, we evaluate the distance between the real and syntezised data distributions (i.e., NO2 concentration values) for each road tra c density class. We propose the use of the distance between distributions according to the KolmogorovSmirnov statistical test. Thus, lower values indicate better sample quality.
Finally, we also consider the computational time and the training epoch the generator created the most accurate pollution distribution (iteration best found ) to evaluate the computational cost of the proposed generative methods.
In order to perform the numerical analysis of our approach, the three CGAN approaches have
been con gured with a learning rate of 0.0002, batch size of 25 samples (108 batches per training
epoch), and 500 training epochs. This section presents the results of performing 30 independent
runs for each CGAN training in National Supercomputing Center (Cluster-UY), Uruguay [
Figure 3 illustrates the evolution of the loss of the generator and the discriminator during the training process. The three approaches show similar behaviour. During the rst 100 epochs, both losses oscillate and increase. This behaviour is explained by the fact that the discriminator is not trained enough to give the proper feedback required by the generator to learn. After that, the discriminator starts becoming stronger and reduces the loss values. Thus, it is harder for the generator to deceive the discriminator. For this reason, the generator begins increasing the computed loss values, allowing the generator to learn how to create more accurate samples. At the end of the training process, the generator and the discriminator have similar loss values, which could indicate that they have reached an equilibrium.
Table 2 summarizes the fake data distributions by showing the median and the interquartile
range (iqr) and Figure 4 illustrates the distributions. The median values of the NO2 generated
distributions are very close to the real ones. However, the diversity (in terms of iqr) of the
fake distributions is substantially lower than in real data. Figure 4 con rms that the fake
distributions are less dispersed than the real ones in Figure 2. This indicates that our methods
are able to capture the general behaviour of the NO2 concentration given the tra c class, but
it has some limitations to capture the whole real distribution. Di erent authors have proposed
methods to improve diversity in GAN training [
(a) CGAN-1 (b) CGAN-2 (c) CGAN-3
Table 3 reports the minimum (min), mean, and standard deviation (std) of the distance between the synthesized data and the real data distributions (min distance), the computation time of each independent run (computational time), and the training epoch the generator created the most accurate pollution distribution (iteration best found ).
min distance min mean
std 0.41 0.42 0.41 0.43 0.01 0.43 0.01 0.43 0.01 computational time
min mean 318.41 677.11 318.99 827.67 341.83 859.05
std 179.07 173.34 106.43 iteration best found min mean
std 21.00 234.61 140.40 51.00 165.13 85.04 20.00 146.10 96.90
In terms of the distance between the generated distributions and the real data (see Table 3), the three proposed CGANs create accurate distributions with the same quality (non-signi cant di erences between them). This is in line with the results showed in Table 2 and Figure 4.
Focusing on the computational cost, on the one hand, CGAN-1, the smallest model, shows the shortest run times. On the other hand, CGAN-3 nds the best generators faster than the others. These results are expected because when training ANNs with the same number of iterations, the computational time increases with the ANN's complexity (i.e., with the number of parameters to train). In turn, bigger networks are able to capture more complex features requiring a lower number of training epochs.
We have proposed using CGANs to train generative models to create synthesized pollution data, in this case, NO2 concentration, according to a given road data tra c density. The idea is to deal with the lack of data su ered by data-driven methods for modelling, predicting, and forecasting ambient air pollution.
We have proposed three di erent CGANs according to the complexity of the ANNs architectures used for the generator and the discriminator. The main results indicate that the three proposed models generate accurate NO2 pollution while requiring a reduced computational time. All the CGANs have shown robustness on the training because all the experiments converged to accurate generators. However, these generative models are limited in terms of producing diverse data samples.
The main lines for future work are related to extend the proposed model to generate the pollution of the whole city of Montevideo by taking into account information from more sensors, de ning the generative modelling problem taking into account other variables such as the weather or the time, and applying the generated data to feed data-driven models to prove that they are able to improve their accuracy after including fake samples.
This research was partially funded by European Unions Horizon 2020 research and innovation program under the Marie Skodowska-Curie grant agreement No 799078, by the European Union H2020-ICT-2019-3 and UMA18-FEDERJA-003, and the Systems that Learn Initiative at MIT CSAIL.