## 4 Machine Learning Methods
### Artificial Neural Network (ANN)  
The artificial neural network is a form of artificial intelligence that mimics the behavior of the human brain and nervous system [35]. ANN can also be learned through the gradient descent of the loss function, namely the back propagation method [36]. ANN is a powerful tool for predicting non-linear problems [37]. The non-linear mapping reinforces the linkages between the input data and the output data [38]. The operational structure of ANN has been described in many studies [39; 40]. Multilayer perceptron is the most widely used ANN type.  
It consists of an input data layer, an output data layer and in the middle is one or more hidden layers [36]. The model complexity is determined by the number of nodes of hidden layers. The input weight matrix is used to link the input layer and the hidden layer. The output weight matrix is used to link the hidden layer and the output layer [41].  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**No** & **D** & **We** & **Cc (\({}^{\rm a}\))** & **Cp** & **S (\({}^{\rm a}\))** & **Mc** & **T (\({}^{\rm a}\))** & **Ac** & **Di** & **L** & **A** & **V** & **M** & **De** & **q\({}_{\rm u}\)** \\ \hline
**Unit** & **m** & **g/cm\({}^{\rm 3}\)** & **-** & **-** & **-** & **\%** & **-** & **kg/cm\({}^{\rm 3}\)** & **cm** & **cm** & **cm\({}^{\rm 2}\)** & **cm\({}^{\rm 3}\)** & **g** & **g/cm\({}^{\rm 3}\)** & **kPa** \\ \hline
1 & 4 & 1.72 & 1 & 7 & 2 & 1.72 & 1 & 100 & 4 & 10 & 19.4 & 194 & 339.8 & 1.75 & 472 \\
2 & 4 & 1.76 & 1 & 7 & 3 & 1.76 & 1 & 100 & 5 & 10 & 19.45 & 194.52 & 333.8 & 1.72 & 498.2 \\
3 & 4 & 1.72 & 1 & 7 & 2 & 1.72 & 1 & 100 & 5 & 10 & 19.63 & 196.35 & 342 & 1.74 & 649.41 \. &. &. &. &. &. &. &. &. &. &. &. &. &. &. \. &. &. &. &. &. &. &. &. &. &. &. &. &. &. &. \. &. &. &. &. &. &. &. &. &. &. &. &. &. &. &. \\
214 & 2 & 1.93 & 2 & 28 & 1 & 1.96 & 2 & 200 & 5 & 10 & 19.43 & 194.26 & 324.4 & 1.67 & 3780.35 \\
215 & 2 & 1.93 & 2 & 28 & 1 & 1.93 & 2 & 200 & 5 & 10 & 19.4 & 194 & 317.8 & 1.64 & 4143.8 \\
216 & 2 & 1.93 & 2 & 28 & 1 & 1.9 & 2 & 200 & 4.9 & 10 & 19.17 & 191.67 & 324.2 & 1.69 & 4922.67 \\ \hline Min & 2.00 & 1.72 & 1.00 & 7.00 & 1.00 & 1.72 & 1 & 100 & 4.00 & 10 & 18.86 & 188.57 & 2488.0 & 1.31 & 2840.6 \\ Average & 3.00 & 1.83 & 1.50 & 17.50 & 1.67 & 1.83 & 2 & 150 & 4.98 & 10 & 19.48 & 194.87 & 336.31 & 1.72 & 1927.87 \\ Max & 4.00 & 1.93 & 2.00 & 28.00 & 3.00 & 1.96 & 3 & 200 & 5.00 & 10 & 19.74 & 197.40 & 385.80 & 1.96 & 5129.83 \\ SD (\({}^{\rm a}\)) & 1.00 & 0.10 & 0.50 & 10.52 & 0.75 & 0.10 & 0.82 & 40.92 & 0.07 & 0.00 & 0.19 & 1.96 & 36.26 & 0.18 & 1215.94 \\ \hline \hline \end{tabular} SD (\({}^{\rm a}\)) = Standard deviation; Cc (\({}^{\rm a}\)): 1—Indoor; 2—outdoor; S (\({}^{\rm a}\)): 1—Yellow clay; 2—Black organic sandy clay; 3—Black sandy clay; T (\({}^{\rm a}\)): 1—Vissai cement; 2—Nghi Son cement; 3—Chinfon Hai Phong cement.  
\end{table}
Table 1: Inputs and output of the present study.  
The output values are compared with the expected values in the set in the training data, errors are calculated and returned to the network. The connection weight is automatically adjusted until the minimum error target is reached [38]. The architecture of ANN model was illustrated in Figure 5.