## 4 Results and Discussions  
As mentioned earlier, many factors directly impact the development of an excellent back-propagation neural network predictive model, especially with a trial and error method, as adopted in this work. They include training algorithm, hidden layers number, neurons number in the hidden layer, transfer function, momentum term, learning rate, etc. Here, the \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Learning Algorithm** & **Weight Adaptation** & **Training Acronym** \\ \hline \multirow{3}{*}{Lavenberg–Marquardt (lm)} & The weight of the lm algorithm is updated via: \(w_{q+1}=w_{q}-(H^{\prime}+\eta I)^{-1}\
abla\epsilon_{q}\) & trainlm \\  & where the Hessian matrix, \(H^{\prime}=J^{T}J\). & \\ \hline \multirow{3}{*}{Bayesian Regularization (br)} & The br approach involves the modification of the performance function, \(\epsilon_{q}\) plus regularisation term & trainbr \\  & \(F(w)=\beta\epsilon_{q}+\alpha\epsilon_{w}\) & trainbr \\  & where \(\beta\) \& \(\alpha\) are special function parameters and a regularisation term, \(\epsilon_{w}=\|w\|^{2}\) & \\ \hline \multirow{3}{*}{Polak–Ribiere Conjugate Gradient (cgp)} & The weight of cgp algorithm is updated by: \(w_{q+1}=w_{q}+a_{q}p_{q}\) & traincgp \\  & With \(p_{q}=-g_{q}+b_{q}p_{q-1}\) and \(b_{q}=\frac{\Lambda g_{q+1}^{T}g_{q}}{g_{q+1}^{T}g_{q-1}^{T}}\) & \\ \hline \multirow{3}{*}{Fletcher-Powell Conjugate Gradient (cgf)} & The weight of scg algorithm is updated by: \(w_{q+1}=w_{q}+a_{q}p_{q}\) & traincgf \\  & With \(p_{q}=-g_{q}+b_{q}p_{q-1}\) and \(b_{q}=\frac{g_{q+1}^{T}g_{q}}{g_{q+1}^{T}g_{q-1}^{T}}\) & \\ \hline \multirow{3}{*}{Scaled Conjugate Gradient (scg)} & The weight of scg algorithm is updated by: \(w_{q+1}=w_{q}+a_{q}p_{q}\) & trainscg \\ \hline \multirow{3}{*}{Resilient Backpropagation (rp)} & With RP algorithm, weight update is by \(w_{q+1}=w_{q}-sign\big{(}\frac{\Delta\epsilon_{q}}{\Delta\epsilon_{q}}\big{)}.\Delta(q)\) & trainrp \\  & where \(\Delta(q)\) = individual step size for weight adaptation & \\ \hline \multirow{3}{*}{BFGS Quasi-Newton (bfg)} & bfg weight update is accomplished via \(w_{q+1}=w_{q}-H^{-1}g_{q}\) & trainbfg \\  & where \(H_{q}^{-1}\) indicates the Hessian matrix inversion on iteration \(q\). & \\ \hline Conjugate gradient with Powell/Beale & The cgb employs update search direction by: \(g_{q-1}g_{q}=0.2\big{\|}g_{q}\big{\|}^{2}\) & traincgb \\ \hline \multirow{3}{*}{Gradient Descent with Adaptive Learning Rate (gda)} & gda weight update is accomplish via \(w_{q+1}=w_{q}+\frac{\Delta\epsilon}{\eta_{q+1}\Delta\epsilon_{q}}q\) & \\  & where \(\alpha\) indicates the user-defined momentum factor and it ranges from 0 to 1 & taingda \\ \hline \multirow{3}{*}{Gradient Descent Variable Learning Rate (gdx)} & With gdx algorithm, weight update is by \(w_{q+1}=w_{q}q_{q+1}-sign\big{(}\frac{\Delta\epsilon_{q}}{\Delta\epsilon_{q}} \big{)}.\Delta(q)\) & traingrdx \\  & where \(\Delta(q)\) = individual step size for weight adaptation and \(\eta_{q}\) & \\  & = variable learning rate & \\ \hline \multirow{3}{*}{One Step Secant (oss)} & With oss algorithm, weight update is by \(w_{q+1}=w_{q}-H_{q}^{-1}g_{q}\) & trainoss \\  & where \(H_{q}\) = Hessian matrix (2 nd derivatives) & \\ \hline \multirow{3}{*}{Gradient Descent with Momentum (gdm)} & gdm weight update is accomplish via \(w_{q+1}=w_{q}-\eta g_{q}+\alpha\frac{\Delta\epsilon}{\Delta\epsilon_{q}-1}\) & traingrdm \\  & where \(\alpha\) indicates the user-defined momentum factor and it ranges from 0 to 1 & \\ \hline \multirow{3}{*}{Gradient Descent (gd)} & With gm algorithm, weight update is by \(w_{q+1}=w_{q}-\eta g_{q}\) & traingd \\  & where \(\eta\) = learning rate & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Respective MLP Network Learning Algorithm. concentration is on the training algorithm, hidden layers number and neurons number in the hidden layer.