## 3 Artificial Neural Network
### Get the Data  
The data that we used to create the ANN model comes from the laboratory tests described in Section 2 herein; \"Materials and Methods\". The test results were saved in the.xlsx format in Excel.  
The data were loaded using the Jupyter notebook and the Python Pandas module. The first five lines of \"raw\" data are presented below (Table 2):  
Our dataset consists of 1227 examples obtained from testing 15 soil samples. All attributes (except \"Test No.\") have numeric values. A summary of all numerical attributes is provided in Table 3.  
After the first look at the data, the next particularly important, but often underestimated, step is to create a test set. The separation of the test set at such an early stage is to prevent the occurrence of a phenomenon called the \"data snooping bias\". When we look at the test set, we can see some interesting pattern (not always right) that will make us choose a specific machine learning model based on it. When dealing with exceptionally large datasets, it is enough to randomly select some examples and put them back to create a test dataset. This is a satisfactory solution, but it does not work well with small datasets. Next time the program runs, a completely different test set is generated. After some time, the person creating the model or the machine learning algorithm itself will see the entire dataset, and this is what we want to avoid. This is why the random seed was used, which allowed to obtain the same pseudorandom test set every time. The test set accounts for 20% of the total data.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Test** & **Cl** & **Si** & **Sa + Gr** & **LL** & **PL** & **IP** & **IL** & **p\({}^{\prime}\)** & **eo** & **OCR** & \(\gamma\) & **G** & **G/Gmax** & **D** \\
**No.** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(-)** & **(\%)** & **(MPa)** & **(-)** & **(\%)** \\ \hline S1 & 14 & 26 & 60 & 22.1 & 11.5 & 10.6 & 0.024 & 50 & 0.40 & 2.8 & 0.0006 & 53.35 & 1.00 & 4.99 \\ S1 & 14 & 26 & 60 & 22.1 & 11.5 & 10.6 & 0.024 & 50 & 0.40 & 2.8 & 0.0009 & 54.63 & 1.00 & 4.99 \\ S1 & 14 & 26 & 60 & 22.1 & 11.5 & 10.6 & 0.024 & 50 & 0.40 & 2.8 & 0.0012 & 54.20 & 1.00 & 5.01 \\ S1 & 14 & 26 & 60 & 22.1 & 11.5 & 10.6 & 0.024 & 50 & 0.40 & 2.8 & 0.0018 & 53.63 & 0.98 & 5.06 \\ S1 & 14 & 26 & 60 & 22.1 & 11.5 & 10.6 & 0.024 & 50 & 0.40 & 2.8 & 0.0024 & 53.35 & 0.98 & 5.11 \\ \hline \hline \end{tabular}  
* Notes: Cl—clay content, Si—slit content, Sa + Gr—sand + gravel content, LL—liquid limit, PL—plasticity limit, IP—plasticity index, IL—liquidity index, p\({}^{\prime}\)—mean effective stress, e\({}_{\text{o}}\)—initial void ratio, OCR—overconsolidation ratio, \(\gamma\)—shear strain, G—shear modulus, G/G\({}_{\text{Gmax}}\)—normalized shear modulus.  
\end{table}
Table 2: First 5 lines of “raw” data from the damping ratio laboratory test.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline  & **Cl** & **Si** & **Sa + Gr** & **LL** & **PL** & **IP** & **IL** & **p\({}^{\prime}\)** & **e\({}_{\text{o}}\)** & **OCR** & \(\gamma\) & **G** & **G/Gmax** & **D** \\ \cline{2-13}  & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** & **(-)** & **(-)** & **(\%)** & **(MPa)** & **(-)** & **(\%)** \\ \hline count & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 & 1227 \\ mean & 17.83 & 35.38 & 46.79 & 33.77 & 15.28 & 18.49 & 0.04 & 193.96 & 0.440 & 1.37 & 0.0117 & 120.75 & 0.87 & 4.57 \\ std & 7.26 & 17.01 & 21.83 & 11.74 & 4.86 & 7.58 & 0.11 & 104.61 & 0.104 & 0.85 & 0.0220 & 76.70 & 0.20 & 2.78 \\ min & 10.00 & 20.00 & 6.00 & 17.70 & 9.10 & 6.60 & \(-\)0.19 & 30.00 & 0.280 & 1.00 & 0.0001 & 6.45 & 0.16 & 1.57 \\
25\% & 14.00 & 23.00 & 17.00 & 24.50 & 12.24 & 12.03 & 0.01 & 110.00 & 0.375 & 1.00 & 0.0008 & 69.82 & 0.81 & 2.57 \\
50\% & 14.00 & 26.00 & 60.00 & 32.75 & 14.26 & 16.79 & 0.02 &