## 5 Conclusions  
In this paper, an LSTM modeling method based on physical mechanism guidance was proposed to predict the dynamic response of vehicle-bridge coupling. The principle of LSTM was introduced, and the conditions required for the method to be used in the surrogate model of vehicle-induced dynamic response analysis were explained. Subsequently, the corresponding LSTM deep neural network structure was constructed. Furthermore, the feasibility of the above method was verified by a small- and medium-span concrete box section of a simply supported railway bridge, and the influence of various factors on the response prediction was analyzed. The main conclusions were as follows:  
1. In terms of the prediction accuracy of different types of responses, in general, the accuracy of displacement prediction was obviously better than that of acceleration, and the prediction of displacement was less affected by various unfavorable factors than that of acceleration. The peak value of acceleration prediction value was smaller than that of theoretical value, and the prediction results were generally strongly correlated with the theoretical value. Therefore, displacement prediction had higher reliability than acceleration prediction;
2. For different dimensional indicators, under the same number of LSTM network layers, as the number of neurons increased, the model evaluation indicators tended to be better, that is, the accuracy of the prediction results tended to increase. However, with the increase in the number of parameters of the neural network model, the nonlinear fitting performance of the model was improved, and it was easy to produce over-fitting phenomena, which led to a decrease in prediction accuracy. When the number of neurons increased from 128 to 256, the trend of each index was different, and some indexes did not change much or even tended to deteriorate;
3. Considering the influence of the noise of axle load and wheelbase on the response prediction, it was found that the noise of the wheelbase had a more significant influence on the prediction, but, in general, the correlation between the predicted response value and the theoretical value was good and the error was controllable. In particular, the displacement prediction performs well under the influence of noise. In addition, with the increase of train speed, the prediction accuracy decreased slightly--in particular, the acceleration prediction was more sensitive. The increase in the number of train sections also reduced the accuracy of response prediction, and the acceleration prediction was more sensitive to the change in train sections.  
Methodology, S.T. and X.K.; software, S.T. and Z.P.; validation, S.T. and J.M.; writing--original draft preparation, S.T. and X.K.; writing--review and editing, S.T., X.K. and J.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Science and Technology Research and Development Project of China State Railway Group Co., Ltd. (L2023G007, L2022G007), Science and Technology Research and Development Program Project of China railway group limited (2020-Special-02, 2021-Special-08), Hunan National Natural Science Foundation (2021 JJ30053), and the Open Foundation of National Engineering Laboratory for High-Speed Railway Construction (HSR202003).  
Not applicable.  
The data presented in this study are available upon request from the corresponding author. The dataset and code cannot be shared due to specific reasons.  
Author [PERSON] was employed by the company China Railway Group Limited. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.