# A Creep Model of Steel Slag-Asphalt Mixture Based on Neural Networks
## 1 Introduction  
The steel industry is fundamental pillar of the national economy in China. A large amount of steel slag is produced during the steel smelting process, but it is not utilized efficiently. However, there is strong demand for asphalt mixture composed of asphalt and conventional aggregates, namely granite and limestone, in constructing asphalt roads. Substituting a portion of these natural aggregates with steel slag not only improves resource utilization efficiency, but also promotes high-quality development within the steel industry. This approach also ensures the environment is protected and carbon emissions are reduced [1; 2; 3]. Previous studies have revealed that steel slag in asphalt pavements effectively delays the onset of surface cracking and enhances resistance to skidding. Additionally, rutting defects on road surfaces are inevitably caused by heavy traffic. Keep, alongside other mechanical properties of steel slag-asphalt mixture, has attracted much attention [4; 5; 6]. In order to describe the creep properties of asphalt mixture, researchers have established various differential or integral models [7; 8; 9]. However, these mathematical models tend to be intricate, due to the complex determination process of model coefficients [10]. More importantly, these models have limited predictive capability to describe creep behaviors under singular influences such as external load levels. Therefore, it is necessary to establish a creep model that takes into account both temperature and stress and has a higher predictive accuracy [11]. Machine learning algorithms, especially artificial neural networks (ANN), have made profound advancements and are increasingly applied to tackle a spectrum of mechanical challenges [12; 13; 14]. In the engineering field, the interrelations among variables can be extraordinarily complex, which often makes it impossible to achieve effective representation through traditional physical or empirical models. Machine learning methodologies are employed by approximating the highly nonlinear mappings that exist between these variables [15]. [PERSON] (2021) [16] has employed machine learning to formulate a predictive model for the creep lifespan of Cr-Mo steels. [PERSON] (2022) [17] has innovatively merged machine learning with finite element analysis to investigate the evolution of contact areas and friction behaviors within nickel-based superalloys under elevated temperatures. [PERSON] (2022) [18; 19] has studied the creep behavior of recycled aggregate concrete (RAC) using machine learning techniques. These scholars reveal the capability of machine learning in evaluating the complex mechanical properties of materials. Using the nonlinear model and adaptive learning ability of ANN, experimental data can be processed efficiently and predict properties of materials effectively. [PERSON] (2019) [20], [PERSON] (2020) [21], and [PERSON] (2010) [22] have each implemented Back Propagation (BP) neural networks to delve into the constitutive relationships within alloy materials. [PERSON] (2022) [23] utilized Long Short-Term Memory (LSTM) neural networks to effectively predict the mechanical dynamics of rubber. Nevertheless, the application of neural network models to the study of the nonlinear mechanical behavior exhibited by steel slag-asphalt mixture remains an area that requires further extensive research. Our study leverages the Long Short-Term Memory (LSTM) architecture, a sophisticated Recurrent Neural Network (RNN) capable of learning from sequences with long-term dependencies [24; 25; 26]. The LSTM's design overcomes the gradient issues inherent in traditional RNNs by incorporating a memory cell with three critical components: the input, forget, and output gates. These gates regulate the flow of information, allowing the network to retain relevant data over time and forget outdated or less important information. The input gate controls the update of the cell state with new information, while the forget gate determines which information to discard from the cell state.