## 2 Data-Driven Modeling
### Artificial Neural Network (ANN)  
Artificial neural networks (ANNs) have a history that dates back to the mid-20 th century, when the mathematical model for the perceptron was first introduced by [PERSON] [74]. The development of the backpropagation algorithm in the 1980s, by [PERSON] et al. [75], improved the training of multi-layer ANNs and led to their widespread use in various fields. Since then, ANNs have continued to evolve, with the development of new architectures and learning algorithms [76]. An artificial neural network (ANN) is a machine learning model that is based on the structure and function of the human brain [76]. Artificial neural networks are composed of interconnected nodes, or artificial neurons, that process information and make predictions in response to inputs. By combining the inputs and the weights assigned to each connection, the interconnected nodes produce an output. There are a number of applications for artificial neural networks, including image classification, speech recognition, and natural language processing, among others. In the field of machine learning and artificial intelligence, they have proven to be effective at solving complex problems. Due to their ability to learn from data and make accurate predictions or classifications based on that data, artificial neural networks (ANNs) have become one of the most powerful tools in the field of machine learning and artificial intelligence [77]. As a result, they simulate the structure and function of the human brain, which is composed of many neurons connected by synapses. Each node or artificial neuron in an ANN, performs simple computations based on the input it receives and the weights assigned to the connections [45]. One neuron's output is then passed on as input to other neurons in the network, allowing the information to be processed and transformed multiple times before it is finally produced. Feedforward, refers to this process of processing and transforming information through multiple layers of neurons. There are various types of artificial neural networks, each designed for a particular task or application. The most popular types of ANNs include feedforward networks, recurrent networks, and convolutional neural networks [78]. An ANN can be used for a variety of purposes, and each type has its own strengths and weaknesses. As the most basic type of ANN, feedforward networks are used for simple tasks, such as binary classification and linear regression. On the other hand, recurrent networks are used for sequences of data, such as speech or text, and are capable of capturing temporal relationships. Image or video analysis can be performed using convolutional neural networks, which are specifically designed to capture the spatial relations between pixels in an image or video. Artificial neural networks (ANNs) can be used to model complex relationships with no established mathematical relationships [79]. The ANN method consists of artificial neurons, and is commonly used to fit nonlinear statistical data. For this purpose, ANN identifies the relationships between input and output parameters based on the strength of the connection between the two neurons, known as the weight. Next, the network seeks to optimize the matrix of weights, which is achieved through practice and adjustment, which is called the paradigm [80]. One of the strongest paradigms, is the backpropagation paradigm. In this study, two backpropagation algorithms are used: (i) the Levenberg-Marquardt (LM) algorithm [81], and (ii) the Bayesian regularization (BR) [82] algorithm. Input, hidden, and output layers are the three main components of ANN architecture. In this study, for each algorithm, i.e., LM and BR, one, two, three, four, and five hidden layers are considered. Log-sig and tan-sig are transfer functions within each neuron. In this study, five different architectures of ANN, with one to five hidden layers, were modelled for each algorithm.