## 2 Materials, Methods and Equipment  
### Artificial Neural Networks  
A mathematical model or computer model that is inspired by the characteristics and structure of biological neural networks is known as an artificial neural network (ANN), and sometimes known as a neural network (NN) [34]. ANNs are powerful, parallel-connected processors that have a natural ability to gather knowledge from experimental data and use that knowledge in a similar way to the human brain [35]. A three-layered structure is present in a neural network (as illustrated in Figure 1). The input layer, which directly communicates with the external environment, is the first layer. The second layer consists of hidden units where computations are performed based on the given function, and the last layer is the output layer that generates the output. The knowledge in neural networks is stored as synaptic weights between neurons. The input data are transmitted from layer to layer through the network until the output data are produced. If the network is a multilayer perceptron using a backpropagation algorithm, and the output is different from the desired output, an error is computed and propagated back through the network. As the error is propagated, the synaptic weights are changed [36]. When compared to statistical methods, ANN analysis is more flexible in terms of the quantity and nature of the training (experimental) data, allowing for the use of less formal experimental designs [37]. Each layer in a neural network has an activation vector, and the accuracy of the network can be affected by parameters such as training data, learning rate, and number of iterations and hidden layers. Figure 1: Structure of ANN [38]. The input layer is denoted by \(a^{(0)}\) and the output layer is denoted by \(a^{(n)}\). Any layers that exist between the input and output layers are considered to be hidden layers. Input layer activation is identical as the input. Each relation between neurons is appointed a unique weight, represented by \(``w\"\). To calculate the output layer, the forward propagation algorithm is used, while the backpropagation algorithm is used for training. Activation functions play a critical role in artificial neural networks, as they facilitate the learning and comprehension of complex, non-linear relationships between input and output data. In an artificial neural network (ANN), the output of each layer is calculated by taking the totality of the products of the inputs and their corresponding weights, followed by the application of a function of activation. This output is then passed as the input to the following layer in the network. The accuracy of neural network predictions depends on the number of layers used and the type of activation function used. A neural network without activation functions acts as a linear regression model with limited performance. The activation function must be differentiable in order to involve backpropagation for error estimation, and finally, weight optimization. There are a large number of activation functions, the most famous of which include binary, linear, sigmoid, tanh, ReLU, exponential, etc. [39]. Rectified Linear Unit, or ReLU (Figure 2), has a derivative function, although it gives the impression of a linear function. ReLU enables backpropagation while making it computationally efficient. The main advantage of the ReLU function is that it does not activate all neurons simultaneously. For a neuron to be deactivated, the output of the linear transformation must be below zero. In other words, the neuron will only deactivate when the output of the linear transformation is exactly zero. This can be mathematically described by Equation (1):  
\[g(Z)=\max(0,Z) \tag{1}\]  
Tanh, short for hyperbolic tangent, is a mathematical function that shares similarities with the sigmoid function. However, unlike the sigmoid function, tanh is symmetric around the origin. This symmetry results in different signs of outputs from previous layers being provided as input to the following layer.