# Long Short-Term Memory Neural Network Applied to Train Dynamic Model and Speed Prediction
## 1 Introduction  
Railway transportation, an effective means to increase the efficiency of energy consumption and relieve the traffic congestion problem, has been stressed as an ideal transport mode in large cities [1]. To achieve safe and efficient operation, train control algorithms remain a key technical issue in the process of the development of railway systems [2]. Traditionally, with the help of signal devices, the train operation is accomplished by skilled drivers. However, this human-based train operation method lacks precise consideration, which may lead to a poor performance of energy consumption, service quality and safety [3]. Recently, with the combination of communication and computer technologies, the automatic train operation has become a research hotspot [4; 5; 6], which also has been used in many newly-built railway systems. Different from the manual labor based method, an automatic train operation system can provide a better operation performance by optimizing train control decisions. Many indicators that describe the running state of the train such as punctuality, riding comfort and energy efficiency can be remarkably improved by automatically adjusting the commands of train accelerating, coasting and braking process. The automatic train operation system mainly solves three arduous tasks: train dynamic model construction [7], speed profile optimization [8] and train speed control [9]. Establishing train dynamic model is regarded as a fundamental and significant problem among these tasks, since all the subsequent studies such as speed profile optimization and train speed control are built on it. Many methods have been proposed to obtain a precise dynamic model [10; 11; 12; 13]. These methods that build upon the Davis formula can be classified into two categories, i.e., single-pointtrain control models and multi-point train control models [10]. In the first one, which has been investigated for many years, the train, consisting of a locomotive and many carriages, is treated as a single-mass model. Although the inner characteristics produced by the coupled system cannot be accurately expressed, this type of model has the advantages of deployment feasibility and calculation simplicity [11]. In the second class, a more complicated model is rigorously designed, which takes the impacts of adjacent carriages into consideration [12]. All of these methods belong to the parametric approaches, where the structure of the model is determined under certain theoretical assumptions and the values of parameters are calculated based on analytical equations, such as [PERSON]'s law and the Davis formula. Nevertheless, a precise train dynamic model is hard to acquire due to unrealistic assumptions and changeable environments [13]. How to obtain an appropriate dynamic model that can reflect the actual condition of train operation remains a crucial task. To find an innovative way to deal with the above-mentioned task, different from the parametric approaches, we propose to apply deep learning algorithms to solve the problem of train dynamic model construction. This kind of data-driven method has been widely investigated in highway trajectory prediction and traffic speed prediction to replace the traditional parametric approach [14; 15; 16]. Data-driven methods also have been introduced for train trajectory tracking [17], train station parking [18] and train operation modeling [19]. Inspired by these studies, in this paper, a long short-term memory (LSTM) neural network is carefully developed to build the train dynamic model in a nonparametric way. LSTM networks [20] are called advanced recurrent neural networks with additional features, which can keep a memory of previous inputs, resulting in a good performance of handling time series problems such as the train dynamic model and the speed prediction.