<p>Ensuring reliable operation in dynamic and uncertain service systems is a major challenge. This study aims to improve service system reliability by predicting reliability in advance to eliminate potential risks, especially addressing the temporal covariate shift problem, and proposes an efficient solution. This paper proposes a service reliability prediction method based on multivariate time series and an improved adaptive recurrent neural network (AdaRNN) model. Multiple reliability indicators, including service response time, service throughput, system response rate, and service reliability, are used to construct multivariate time series to represent service reliability, while the improved AdaRNN model is employed to effectively handle the temporal covariate shift problem. The improved AdaRNN model utilizes a dynamic programming algorithm to achieve optimal temporal domain partitioning and employs the self-attention mechanism to learn the multivariate temporal features and their interrelationships. The model learns the maximum similarity of multivariate temporal features from different time domains during the training phase, and then, by applying the concept of temporal domain adaptation, it is used for the prediction task on the test set. To support large-scale multivariate time-series data and enable efficient training of the improved AdaRNN model, this work utilizes high-performance computing (HPC) infrastructure. The computational demands of model training, temporal domain adaptation, and multivariate sequence alignment make HPC resources essential for ensuring real-time performance and model scalability across diverse service systems. The experimental results show that the proposed service reliability prediction method, based on transfer learning, demonstrates excellent robustness in predicting reliability across different services. Additionally, it outperforms mainstream methods in terms of both accuracy and model adaptation ability.</p>