## 1 Introduction
The first part of the paper examines the prediction performance of three-layer BP-ANN models with various node numbers in the hidden layer, to reveal the correlation among the node numbers of input and output layers, the ratio of the number of variables contributing above 90% to the response to the total number of variables, and the node number of the hidden layer for each response. In the second part, several combinations of variables were tested as inputs for given three-layer BP-ANN models to assess the influence of the ratio of input variables to the total number of variables on the prediction performance. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Research Field**} & \multirow{2}{*}{\(N_{ratio}\)} & \multirow{2}{*}{\(N_{i}\)} & \multirow{2}{*}{\(N_{ratio}\)} & \multirow{2}{*}{\(N_{i}\)} & \multirow{2}{*}{\(N_{i}\)} & \multirow{2}{*}{\(N_{i}\)} & \multirow{2}{*}{\(N_{i}\)} & \multirow{2}{*}{**Number**} & \multicolumn{2}{*}{**Optimal**} & \multicolumn{2}{*}{**Equation**} & \multicolumn{2}{*}{**Equation**} & \multicolumn{2}{*}{**Equation**} & \multicolumn{2}{*}{**Equation**} & \multicolumn{2}{*}{**Equation**} & \multicolumn{2}{*}{**Equation**} \\  & & & & & & & & & & & & & & & & & \\ \hline
**Erosion of beaches [13]** & 105 & 3 & 35 & 15 & 1–20 & 20 & 3 & [5, 15] & [4, 15] & 4, 5 & 26, 27 & 19, 20 & 17 \\ \hline
**Energy conservation in old buildings [14]** & 66 & 7 & 9.4 & 1 & 4–15 & 12 & 15 & [3, 13] & [2, 13] & 2, 3 & 8, 9 & 12, 13 & 5, 6 \\ \hline
**Power output [15]** & – & 5 & – & 1 & 1–11 & 11 & 7 & [3, 13] 1  & 2, 3 & – & – & – & 4.5 \\ \hline
**Hyporemediation of palm oil secondary** & 30 & 3 & 10 & 2 & 1–15 & 15 & 13 & [3, 13] 1  & 2, 13  & 2, 3 & 7,8 & 7,8 & 4 \\ \hline
**Absorption of metal ions [17]** & 13 & 3 & 4.3 & 3 & 1–15 & 15 & 14 & [4, 14] 1  & 3,14  & 2,3 & 3,4 & 6,7 & 5 \\ \hline
**Extraction of sensing information [18]** & 500 & 100 & 5 & 1 & 11–20 & 10 & 19 & [11, 20] 1  & 10,11 & 4,5 & 72,73 & 67,68 \\ \hline
**Lithology identification for shale oil reservoir [19]** & 220 & 11 & 20 & 4 & 7–11 & 5 & 10 & [4, 14]1  & 3, 4 & 18,19 & 22,23 & 11,12 \\ \hline
**Moisture content prediction in paddy drying forces [20]** & – & 3 & – & 1 & 2–12 & 11 & 2 & [3, 12] 1  & 2,2 1  & - & – & 3 \\ \hline
**Corn variety identification [21]** & – & 10 & – & 3 & 3–14 & 12 & 8 & [4, 14] 1  & 3,4 & – & – & – & 9,10 \\ \hline
**Mechanical behavior of mortar [22]** & 30 & 6 & 5 & 1 & 1–9 & 9 & 2 & [3, 13] 1  & 2,3 1  & 4,5 & 8,9 & 5 \\ \hline
**Extraction of phenolic compounds [23]** & 12 & 3 & 4 & 1 & 1–3 & 3 & 2 & [3, 12] 1  & 2,2 1  & 3, 7 & 5,6 & 3 \\ \hline
**Damage pattern of structural systems [24]** & 113 & 10 & 11.3 & 4 & 17,18 & 2 & 17 & [4, 14] 1  & 3,4 & 10,11 & 17,18  & 10,11 \\ \hline \hline \end{tabular} \(N_{ratio}\) is the dataset size for training.  
\(N_{i}\), \(N_{i}\), \(N_{i}\) are the nodes numbers in the input, hidden, and output layer, respectively.  
\(\quad\) – Data are not available in the literature.  
\(\quad\) – The rule was used to define modes number in the hidden layer by the authors in their publication.  
\(\quad\) – A Rules that optimal \(N_{i}\) are coincident with.  
\end{table} 
Table 1: Literature study of rules to define the node number in the hidden layer.