# Data-Driven Approaches for Predicting and Forecasting Air Quality in Urban Areas
## 2 Materials and Methods
### DL Custom-Made Algorithms for AQI
The model parameters are the neurons connections weights (for instance, for the first Conv1D layer), weights of shape are (2, 1, 4) with associated weight matrix [\([-0.585093,\)\(-0.42209578,\)\(-0.10097494,\)\(0.888292724];\)\([-0.65418446,\)\(0.56988806\)\(0.11362608,\)\(0.11557351]\)], and the bias for each neuron (for instance, the biases shape for the first Conv1D layer) is (4), and the corresponding biases vector is [\(0,\)\(0.05134838,\)\(-0.0748504,\)\(0.0022911\)];
3. Recurrent Neural Networks (RNNs) handle sequential data by incorporating cycles in their architecture, allowing information to persist. This feature enables RNNs to maintain a form of memory. Standard RNNs face challenges with long-term dependencies because of problems such as vanishing and exploding gradients [87,88]. In this case, the hyperparameters that define the RNN architecture are three SimpleRNNs layers (the first one representing the input layer-input shape that defines the shape of the input data for the RNN layers, with 32 RNN units with a return sequence; the second one with 128 units with a return sequence and the third one with 256 units without a return sequence, the output of each RNN layer using ReLu-type activation function), a dropout layer to prevent overfitting with a dropout rate of 0.2, and an output layer (a dense one) with just one neuron. Other hyperparameters have the same values as those of FNNs and TCNs. The model parameters are the neurons connections weights (for instance, for the first SimpleRNNslayer) the weights shape is (1, 32) with associated weight matrix [\(-0.37684393,\)\(-0.3347999,\)\(0.12421719,\)\(0.04884235,\)\(0.40717593,\)\(-0.2224836,\)\(0.11467709,\)\(-0.44855782,\)\(\ldots,0.24549635,\)\(-0.4644161,\)\(0.14050183,\)\(-0.421698,\)\(0.4127007,\)\(0.20661259,\)\(-0.17216238,\)\(-0.0187266\)], and the biases shape for each neuron (for instance, the biases shape for the first SimpleRNN layer) is (32) with the corresponding vector bias [\(0.20325282,\)\(0.01771547,\)\(0.27512175,\)\(\ldots,0.12933277,\)\(0.10233897,\)\(-0.00640139\)];
4. LSTMs are a form of RNN featuring memory cells and gating mechanisms that manage the flow of information. This architecture is used for tasks requiring the retention of information over extended periods, such as speech recognition and natural language processing [87,89,90]. In this case, the hyperparameters that describe this type of network architecture are two LSTM layers (the first LSTM layer contains the input shape, each one with 100 neurons, with ReLu-type used activation function, first LSTM layer with a return sequence and the second one without a return sequence), two dropout layers (with a dropout rate of 0.2 to prevent overfitting), and one output layer (a dense one, with just one neuron). Other hyperparameters have the same values as FNNs, TCNs, and RNNs. The model parameters are the neuron connection weights (for instance, for the last layer, the dense one), the weight matrix is (100, 1)(respectively, [[\(-\)0.1917704], \(\ldots\), [0.03949241]]), and the bias shape of the dense layer is (1), a 1D array ([0.34271002]). * General Regression Neural Networks (GRNNs) are FNNs designed for regression tasks. They utilize a kernel-based approach to estimate the output for a given input, used for problems where the relationship between input and output is not strictly linear [85; 91]. The hyperparameters that define the FNN architecture are five dense layers (hidden layers--dense ones, the first one representing the input layer with 64 units, the second one with 128 units, the third and the fourth layer with 256 units, and the fifth layer with 64 units, all dense layers using Radial Basis Function (RBF) activation function), one dropout layer to prevent overfitting with dropout rate 0.2 and, and an output layer (a dense one) with just one neuron. Other hyperparameters have the same values as FNNs, TCNs, RNNs, and LSTMs.