## 1 Introduction  
With the development of intelligent transportation systems, sensor technology, computer technology, and other advanced technologies have found increasing applications in the field of transportation. However, these technologies are still insufficient to meet the demands of intelligent transportation development, and traffic congestion and accidents remain major issues that need to be addressed [1; 2]. Traffic flow prediction, as a crucial component of intelligent transportation systems, can help with traffic light phase control, dynamic path planning for vehicle navigation, and other aspects that can reduce accidents, alleviate traffic congestion, and improve traffic conditions. Over the years, traffic flow prediction methods have evolved with advancements in technology. The rapid development of sensing technology has made it easier to capture traffic flow data, providing a more substantial dataset for forecasting purposes [3; 4; 5; 6]. Traffic flow data are often obtained through video detection, microwave sensors, etc. Traffic flow, as time series data, tends to show a predictable pattern of change within a day. However, factors such as holidays and weather can cause fluctuations and changes in traffic flow, making it challenging to predict accurately. In the past, autoregressive integrated moving average (ARIMA) models were commonly used for traffic flow prediction due to their simplicity and effectiveness [7; 8; 9]. However, these models are unable to capture the nonlinear features present in traffic flow, resulting in mediocre prediction performance. Similar problems also lie in the support vector regression (SVR) and k-nearest neighbors (KNN) models. With the development of deep learning, convolutional-neural-network-basedprediction methods [10] and recurrent-neural-network-based prediction methods [11; 12] have been employed for traffic flow prediction. These models are capable of extracting internal features of traffic flow and grasping the traffic flow change pattern more effectively than previous methods, achieving good results in short-term traffic flow prediction. In particular, LSTM [11] neural network is widely used in short-term traffic flow prediction but may not be suitable for long series prediction. The introduction of transformer [13] has led to widespread attention on self-attention, resulting in numerous models derived on this basis for long series prediction, providing new ideas for the development of our traffic flow prediction. Adequate and effective data features are key to improving the accuracy of prediction models. To delve deeper into the internal change patterns of traffic flow data and enhance the model's ability to extract data features, some researchers have utilized data decomposition methods to assist prediction models for time series prediction, such as wavelet decomposition and empirical mode decomposition (EMD) [14], which have achieved better prediction results than single models. However, while wavelet decomposition is less adaptive, EMD and its improved algorithms suffer from endpoint effects and over-envelope problems. Variational mode decomposition (VMD) [15] is an adaptive, fully recursive modal variational method that can address these issues and more effectively decompose single traffic flow data into multiple components with different frequencies. This facilitates the model to fully extract the internal features of the data and achieve more accurate prediction results. Given VMD's excellent data decomposition ability and the auto-correlation mechanism's advantage for long-term prediction, we developed a sequence-to-sequence hybrid model for traffic flow prediction.