## 3 Methodology
### Model Construction
#### 3.3.3 Artificial Neural Network Background and Modeling  
It is widely accepted that ANNs are a technology that offer an alternative method for resolving complicated and ill-defined situations. An artificial neural network (ANN) is a type of information-processing model that simulates how the human brain processes data. This information processing system's architecture is made up of highly interconnected processing units called neurons that operate in parallel to address issues. Neural networks are useful when creating extremely complex algorithms or when identifying patterns in the data that already exist is necessary [110].  
By definition, a neural network is a system of basic processing units known as neurons that are linked to a network by a set of weights (Figure 4). In Figure 4, the * sign indicates multiplication. It is affected by the processing element's mode of operation, the weights' sizes, and the network's architecture. Neurons are processing elements that take in many inputs (p), weigh them (w), add a bias (b), add them all up, and then use the result as an argument for a transfer function (f), which is a single-valued function. This procedure results in the neuron's output (a).  
In the most popular networks, the neurons are arranged in layers, with each layer's neurons only accepting input from the preceding layer's neurons or from outside sources. A collection of examples showing how the output relates to the inputs is required in order to calculate the weight values. As a result, a set of data is generated that describes the system's whole working range. Gender, age, level of education, school level, teaching  
Figure 4: A full connected neural network’s scheme, showing an example of a single neuron, two layers (L1 with three neurons and L2 with one), one output element, and four input elements [111].  
experience, and creative thinking disposition are chosen as the input variables for the neural network that is created. Teachers' MPSBs are the output variable.  
The weight values of the neural network have information contained in them. Training is the process of figuring out the weights from these samples; it is essentially a traditional estimate problem. The most popular approach for this goal is back-propagation, which is employed here. It tends to provide logical responses to inputs that it has never seen before.  
In conventional back-propagation, the network weights are changed along the performance function's negative gradient via a gradient descent method. The process of calculating the gradient for non-linear multiple-layer networks is known as back-propagation. The mean sum of the squares of the network errors between the network outputs and the goal outputs is the common performance function used to train feed-forward neural networks [112]. The training function in this work was the batch gradient descent algorithm [113].  
Following network training, the model must be validated using a representative subset of data that were not utilized in the model's training.  
The root mean square error (RMSE) and determination coefficient (\(R^{2}\)) between the modeled output and metrics from the training and validation datasets were used to assess the neural network model's performance. A model is considered very good when the \(R^{2}\) is high, \(\geq\)0.8, and the RMSE is at its lowest [114]. The neural network model's design was optimized through the application of varying numbers (1-10) of hidden neurons.