## 2 Materials and Methods
### Methodology of Artificial Neural Network Modeling  
ANN can be described as a form of artificial intelligence within computing systems designed to process information in a manner analogous to the neural processing observed in the human brain [26]. The primary strength of ANNs lies in their ability to model complex, non-linear, and multidimensional functional relationships without requiring prior assumptions about these relationships. By leveraging self-organizing capabilities, they learn directly from empirical data, making them particularly well suited for capturing the behavior of nonlinear, multivariable systems--both static and dynamic [27].  
The ANN approach, noted for its ability to learn from complex, nonlinear, and multidimensional data, is widely applied to prediction, classification, and optimization tasks. By generalizing from large training sets, ANNs can serve as \"black-box\" models for multivariable static and dynamic processes. Modeled after the human brain, a typical ANN comprises three layers--input, hidden, and output--each including a weight matrix, a bias vector, and an output vector that are able to capture intricate input-output relationships [28].  
The transfer function of each layer in ANN, along with the interconnections between layers and neurons, plays a vital role in information processing. Commonly employed transfer functions in ANNs include linear (purelin), sigmoid or log-sigmoid, and hyperbolic tangent sigmoid functions. The dataset is typically partitioned into three subsets: training, validation, and testing. During training, the objective is to adjust the synaptic weights of the network to achieve a stable state. For model accuracy, the training data must be representative of the overall problem, as its characteristics critically influence the network's learning performance [29; 30].  
In the proposed ANN model, the input parameters--heating rate (\({}^{\circ}\)C/min) and temperature (\({}^{\circ}\)C)--were employed to predict weight loss (%) behavior. This study utilized over 7000 lines of experimental TGA data. Following standard practice, 80% of the dataset was allocated for training, while the remaining 20% was reserved for validation. During training and validation, the dataset was split according to its features and via random selection, respectively. The ANN architecture, along with its corresponding input and output parameters, is illustrated in Figure 2. Further details regarding the ANN configuration used in this study are provided in Section 3.2.  
In the estimation of thermodynamic parameters using ANN, activation energy values predicted through the ANN-assisted implementation of the Friedman method were employed as inputs for the corresponding thermodynamic equations. The experimentally determined thermodynamic functions were derived based on activation energy values obtained from the application of the Friedman method to non-isothermal TGA data. The Friedman method's differential, model-free nature and high resolution make it well-suited for complex degradation systems, as its ability to yield accurate, conversion degree-specific activation energies enhance the reliability of thermodynamic parameter estimation and provides deeper insight into thermal degradation mechanisms.  
Figure 2: (a) ANN structure and (b) flowchart of ANN.