## 3 Concept and Methodology
### Machine Learning and Data
\[h_{i}^{(1)}=\Omega^{(1)}\left(\sum_{j}w_{ij}^{(1)}x_{j}+b_{i}^{(1)}\right);h_{ i}^{(2)}=\Omega^{(2)}\left(\sum_{j}w_{ij}^{(2)}x_{j}+b_{i}^{(2)}\right);y_{i}= \Omega^{(3)}\left(\sum_{j}w_{ij}^{(3)}x_{j}+b_{i}^{(3)}\right) \tag{4}\]  
where \(h_{i}^{(1)}\) represents units in the \(n\)th hidden layer, \(x_{j}\) input units or features, \(b_{i}^{(1)}\) bias, \(\sum\limits_{j}w_{ij}^{(1)}\) weight, \(\Omega^{(1)}\) activation functions, and \(y_{i}\) output unit. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**INPUT**} & & & **OUTPUT** \\ \hline  & & & Configuration 1 & Configuration 2 & & Configuration 3 & \\ \hline \multirow{3}{*}{\(\theta_{i}\) (\({}^{\circ}\))} & Air/water & \multirow{3}{*}{\(T\) (\({}^{\circ}\)C)} & Distance \(d\) & \multirow{3}{*}{\(\lambda\) (nm)} & Distance \(d\) & \multirow{3}{*}{\(\lambda\) (nm)} & Distance \(d\) & \\  & concentration & & (cm) & & (cm) & & (cm) & & (cm) & \\ \hline
42.5 & 15/5 & 30 & 16.668650 & 450 & 16.67984 & 520 & 16.69381 & 660 & 0 \\
8.5 & 14/6 & 30 & 2.7557548 & 450 & 2.757758 & 520 & 2.760128 & 660 & 1 \\
14.5 & 13/7 & 50 & 4.6986000 & 450 & 4.702555 & 520 & 4.707375 & 660 & 0 \\
18 & 14/6 & 50 & 5.9764883 & 450 & 5.980795 & 520 & 5.986045 & 660 & 0 \\
23 & 10/10 & 40 & 7.2846954 & 450 & 7.294368 & 520 & 7.306362 & 660 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Input-output data set sample. The used (MLP) multilayer perceptron classifier model contains 13 hidden layers and employs the Hyperbolic Tangent activation function with two random states. The input layer has 3054 data samples plus 10 more samples for tuning. Strategies used to forestall over-fitting in MLP are model decision, early consummation, weight decay, and pruning [28]. Because MLPs are universal function approximations, as demonstrated by [PERSON]'s theorem, they can be used to construct mathematical models using regression analysis. MLPs produce good classification algorithms because classification is a specific case of change because the response variable is categorical. The multilayer perceptron (MLP) model is an artificial neural network that maps input data sets to a set of corresponding outputs. As previously cited, an MLP consists of several layers of nodes in a directed graph, with each layer being fully interconnected with the others. In addition to the input, each node is a neuron (as a processing element) with a nonlinear activation function. MLP uses a managed learning technique called back-propagation to train the network. MLP is a modification of the standard linear perceptron and identifies nonlinearly separated data. Figure 4 summarizes all of the mentioned parts of the methodology. Figure 4 is a flowchart that systematically explains the research flow, highlighting all important points involved in data collection or simulation, data set formation, and machine learning modeling. To verify the model results or predictions, a variety of error parameters are determined with the primary focus on the mean absolute error (MAE), root mean squared error (RMSE), and R-squared. \[\text{MAE}=\frac{1}{m}\sum_{k=1}^{m}\left|y_{k}-_{k}\right| \tag{5}\]  
where \({}_{k}\) are the predicted values for interval \(k\) and \(y_{k}\) represents the real output. Similarly, the RMSE formula is given as:  
\[\text{RMSE}=\sqrt{\frac{1}{m}\sum_{k=1}^{m}\left(y_{k}-_{k}\right)^{2}} \tag{6}\]  
Both MAE and RMSE describe a typical model assumption, both with the units of the variable of interest, where the two estimates can range from 0 to \(\infty\), and are aloof in regards to the course of bumbles. They are known as conversely organized scores, and they imply that lower scores address a predominant model [60; 61].