CMAGIN A Channel-aware Multi-scale Adaptive Graph Interaction Network for Multivariate Time Series Forecasting
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Published
Nov 20, 2025
Weipeng Liu
Bowen Shi
Jixuan Wang
Xiangyu Hu
Xiaofei Xue
Haixing Zhu
Abstract
Multivariate time series (MTS) data is widely utilized in industrial manufacturing, equipment maintenance, and health monitoring. However, the high dimensionality, dynamic nature, and heterogeneity characteristics bring significant challenges for modeling. Traditional deep learning algorithms based on sequential modeling struggle to capture the complex structural relationships between different time series variables, making it difficult to uncover interaction patterns and potential dependencies. To address the dynamic and complex dependencies among variables in MTS data and further balance the importance distribution across multiple temporal feature channels, this work proposes a channel-aware multi-scale adaptive graph interaction network (CMAGIN) for MTS forecasting. The proposed framework integrates a dynamic and adaptive graph constructor with local awareness and global attention (DAGC-LAGA) and a channel-wise adaptive center enhancement (CACE) mechanism. The design of DAGC-LAGA captures sparse neighborhood relations through a multi-view local dynamic graph constructor and further leverages a global attention graph enhancer to model semantic correlations. The results effectively display dynamic dependencies among variables. The introduction of the CACE module dynamically enhances key node features by calculating the node importance at the channel level. In addition, applying the centrality-aware attention mechanism improves the sensitivity of the model to crucial temporal patterns. Furthermore, the results are verified via the C-MAPSS dataset for aircraft engine degradation prediction. Experimental results demonstrate that the CMAGIN model outperforms comparative methods in both RMSE and Score metrics, and exhibits robust performance under complex operating conditions and multiple-fault scenarios. Future research could investigate scalable applications of CMAGIN across diverse industrial scenarios to enable field deployment of intelligent operation and maintenance systems.
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Keywords
graph neural network, remaining useful life prediction, multivariate time series
References
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Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage propagation modeling for aircraft engine run-to-failure simulation. In Proceedings of the 2008 International Conference on Prognostics and Health Management, 1-9.
Shih, S. Y., Sun, F. K., & Lee, H. y. (2019). Temporal pattern attention for multivariate time series forecasting. Machine Learning, 108(8-9), 1421-1441. doi:10.1007/ s10994-019-05815-0
Tarmanini, C., Sarma, N., Gezegin, C., & Ozgonenel, O. (2023). Short term load forecasting based on ARIMA and ANN approaches. Energy Reports, 9, 550-557. doi:10.1016/j.egyr.2023.01.060
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Wang, Y., Wu, M., Li, X., Xie, L., & Chen, Z. (2023). Multivariate time-series representation learning via hierarchical correlation pooling boosted graph neural network. IEEE Transactions on Artificial Intelligence, 5(1), 321-333.
Wang, Y., Xu, Y., Yang, J., Chen, Z., Wu, M., Li, X., & Xie, L. (2023). Sensor alignment for multivariate time-series unsupervised domain adaptation. In Proceedings of the AAAI conference on artificial intelligence, 37(8), 10253-10261.
Wang, Y., Xu, Y., Yang, J., Wu, M., Li, X., Xie, L., & Chen, Z. (2024). Fully-connected spatial-temporal graph for multivariate time-series data. In Proceedings of the AAAI conference on artificial intelligence, 38(14), 15715-15724.
Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., & Yu, P. S. (2021). A Comprehensive Survey on Graph Neural Networks. IEEE Transactions on Neural Networks and Learning Systems, 32(1), 4-24. doi:10.1109/TNNLS. 2020.2978386
Wu, Z., Pan, S., Long, G., Jiang, J., & Zhang, C. (2019). Graph WaveNet for Deep Spatial-Temporal Graph Modeling. In Proceedings of the 28th International Joint Conference on Artificial Intelligence, 1907–1913.
Xiao, Y., Yin, H., Zhang, Y., Qi, H., Zhang, Y., & Liu, Z. (2021). A dual‐stage attention‐based Conv‐LSTM network for spatio‐temporal correlation and multivariate time series prediction. International Journal of Intelligent Systems, 36(5), 2036-2057.
Xu, K., Hu, W., Leskovec, J., & Jegelka, S. (2018). How powerful are graph neural networks?. arxiv preprint arxiv:1810.00826.
Xu, N., Kosma, C., & Vazirgiannis, M. (2023). TimeGNN: Temporal Dynamic Graph Learning for Time Series Forecasting. In International Conference on Complex Networks and Their Applications, 87–99.
Yu, B., Yin, H., & Zhu, Z. (2018). Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting. In Proceedings of the 27th International Joint Conference on Artificial Intelligence, 3634–3640.
Yu, H., Li, T., Yu, W., Li, J., Huang, Y., Wang, L., & Liu, A. (2022). Regularized Graph Structure Learning with Semantic Knowledge for Multi-variates Time-Series Forecasting. In Proceedings of the 31st International Joint Conference on Artificial Intelligence, 2362–2368.
Zhou, H., Zhang, S., Peng, J., Zhang, S., Li, J., Xiong, H., & Zhang, W. (2021). Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting. In Proceedings of the 35th AAAI Conference on Artificial Intelligence, 35(12), 11106-11115.
Zhou, T., Ma, Z., Wen, Q., Wang, X., Sun, L., & Jin, R. (2022). FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting. In Proceedings of the International Conference on Machine Learning, 162, 27268-27286.
Bai, L., Yao, L., Li, C., Wang, X., & Wang, C. (2020). Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting. Advances in Neural Information Processing Systems, 33, 17804-17815.
Casolaro, A., Capone, V., Iannuzzo, G., & Camastra, F. (2023). Deep Learning for Time Series Forecasting: Advances and Open Problems. Information, 14(11), 598. doi:10.3390/info14110598
Chen, L., Chen, D., Shang, Z., Wu, B., Zheng, C., Wen, B., & Zhang, W. (2023). Multi-scale adaptive graph neural network for multivariate time series forecasting. IEEE Transactions on Knowledge and Data Engineering, 35(10), 10748-10761.
Chen, W., Wang, Y., Du, C., Jia, Z., Liu, F., & Chen, R. (2023). Balanced Spatial-Temporal Graph Structure Learning for Multivariate Time Series Forecasting: A Trade-off between Efficiency and Flexibility. In Proceedings of the Asian Conference on Machine Learning, 189, 185-200.
Ding, C., Sun, S., & Zhao, J. (2023). MST-GAT: A multimodal spatial-temporal graph attention network for time series anomaly detection. Information Fusion, 89, 527-536. doi:10.1016/j.inffus.2022.08.011
Feng, C., Shao, L., Wang, J., Zhang, Y., & Wen, F. (2025). Short-term Load Forecasting of Distribution Transformer Supply Zones Based on Federated Model-Agnostic Meta Learning. IEEE Transactions on Power Systems, 40(1), 31-45. doi:10.1109/TPWRS.2024.33930 17
Gao, H., Liu, Y., & Ji, S. (2021). Topology-aware graph pooling networks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43(12), 4512-4518.
Gao, X., Dai, W., Li, C., Xiong, H., & Frossard, P. (2021). ipool—information-based pooling in hierarchical graph neural networks. IEEE Transactions on Neural Networks and Learning Systems, 33(9), 5032-5044.
Guo, Q., He, Z., & Wang, Z. (2024). Monthly climate prediction using deep convolutional neural network and long short-term memory. Scientific Reports, 14(1), 17748. doi:10.1038/s41598-024-68906-6
He, Z., Xu, L., Yu, J., & Wu, X. (2024). Dynamic multi-fusion spatio-temporal graph neural network for multivariate time series forecasting. Expert Systems with Applications, 241. doi:10.1016/j.eswa.2023.122729
He, Z., Zhao, C., & Huang, Y. J. A. S. (2022). Multivariate time series deep spatiotemporal forecasting with graph neural network. Applied Sciences, 12(11), 5731.
Huang, R., Huang, C., Liu, Y., Dai, G., & Kong, W. (2020). LSGCN: Long Short-Term Traffic Prediction with Graph Convolutional Networks. In Proceedings of the 29th International Joint Conference on Artificial Intelligence, 7, 2355-2361
Huo, G., Zhang, Y., Wang, B., Gao, J., Hu, Y., & Yin, B. (2023). Hierarchical Spatio-Temporal Graph Convolutional Networks and Transformer Network for Traffic Flow Forecasting. IEEE Transactions on Intelligent Transportation Systems, 24(4), 3855-3867. doi:10.1109/TITS.2023.3234512
Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: principles and practice: OTexts.
Jin, M., Koh, H. Y., Wen, Q., Zambon, D., Alippi, C., Webb, G. I., King, I., Pan, S. (2024). A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(12), 10466-10485. doi:10.1109/tpami.2024.3443141
Kim, J., Lee, H., Yu, S., Hwang, U., Jung, W., & Yoon, K. (2023). Hierarchical Joint Graph Learning and Multivariate Time Series Forecasting. IEEE Access, 11, 118386-118394. doi:10.1109/ACCESS.2023.3325041
Kim, J., Oh, S., Kim, H., & Choi, W. (2023). Tutorial on time series prediction using 1D-CNN and BiLSTM: A case example of peak electricity demand and system marginal price prediction. Engineering Applications of Artificial Intelligence, 126. doi:10.1016/j.engappai.2023.106817
Kipf, T. N., & Welling, M. J. a. p. a. (2016). Semi-supervised classification with graph convolutional networks. arxiv preprint arxiv:1609.02907.
Lai, G., Chang, W. C., Yang, Y., & Liu, H. (2018). Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks. In Proceedings of the 41st International ACM SIGIR Conference on Research & Development in Information Retrieval, 95-104.
Li, S., & Cai, H. (2024). Short-Term Power Load Forecasting Using a VMD-Crossformer Model. Energies, 17(11), 2773. doi:10.3390/en17112773
Li, T., Zhao, Z., Sun, C., Yan, R., & Chen, X. (2021). Hierarchical attention graph convolutional network to fuse multi-sensor signals for remaining useful life prediction. Reliability Engineering & System Safety, 215, 107878.
Liu, Y., Liu, Q., Zhang, J.-W., Feng, H., Wang, Z., Zhou, Z., & Chen, W. (2022). Multivariate Time-Series Forecasting with Temporal Polynomial Graph Neural Networks. Advances in Neural Information Processing Systems, 35, 19414-19426.
Pareja, A., Domeniconi, G., Chen, J., Ma, T., Suzumura, T., Kanezashi, H., Kaler, T., Schardl, T., & Leiserson, C. (2020). EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs. In Proceedings of the 34th AAAI Conference on Artificial Intelligence, 34(04), 5363-5370.
Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage propagation modeling for aircraft engine run-to-failure simulation. In Proceedings of the 2008 International Conference on Prognostics and Health Management, 1-9.
Shih, S. Y., Sun, F. K., & Lee, H. y. (2019). Temporal pattern attention for multivariate time series forecasting. Machine Learning, 108(8-9), 1421-1441. doi:10.1007/ s10994-019-05815-0
Tarmanini, C., Sarma, N., Gezegin, C., & Ozgonenel, O. (2023). Short term load forecasting based on ARIMA and ANN approaches. Energy Reports, 9, 550-557. doi:10.1016/j.egyr.2023.01.060
Wang, H., Zhang, W., Yang, D., & Xiang, Y. (2023). Deep-Learning-Enabled Predictive Maintenance in Industrial Internet of Things: Methods, Applications, and Challenges. IEEE Systems Journal, 17(2), 2602-2615. doi:10.1109/JSYST.2022.3193200
Wang, Y., Wu, M., Li, X., Xie, L., & Chen, Z. (2023). Multivariate time-series representation learning via hierarchical correlation pooling boosted graph neural network. IEEE Transactions on Artificial Intelligence, 5(1), 321-333.
Wang, Y., Xu, Y., Yang, J., Chen, Z., Wu, M., Li, X., & Xie, L. (2023). Sensor alignment for multivariate time-series unsupervised domain adaptation. In Proceedings of the AAAI conference on artificial intelligence, 37(8), 10253-10261.
Wang, Y., Xu, Y., Yang, J., Wu, M., Li, X., Xie, L., & Chen, Z. (2024). Fully-connected spatial-temporal graph for multivariate time-series data. In Proceedings of the AAAI conference on artificial intelligence, 38(14), 15715-15724.
Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., & Yu, P. S. (2021). A Comprehensive Survey on Graph Neural Networks. IEEE Transactions on Neural Networks and Learning Systems, 32(1), 4-24. doi:10.1109/TNNLS. 2020.2978386
Wu, Z., Pan, S., Long, G., Jiang, J., & Zhang, C. (2019). Graph WaveNet for Deep Spatial-Temporal Graph Modeling. In Proceedings of the 28th International Joint Conference on Artificial Intelligence, 1907–1913.
Xiao, Y., Yin, H., Zhang, Y., Qi, H., Zhang, Y., & Liu, Z. (2021). A dual‐stage attention‐based Conv‐LSTM network for spatio‐temporal correlation and multivariate time series prediction. International Journal of Intelligent Systems, 36(5), 2036-2057.
Xu, K., Hu, W., Leskovec, J., & Jegelka, S. (2018). How powerful are graph neural networks?. arxiv preprint arxiv:1810.00826.
Xu, N., Kosma, C., & Vazirgiannis, M. (2023). TimeGNN: Temporal Dynamic Graph Learning for Time Series Forecasting. In International Conference on Complex Networks and Their Applications, 87–99.
Yu, B., Yin, H., & Zhu, Z. (2018). Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting. In Proceedings of the 27th International Joint Conference on Artificial Intelligence, 3634–3640.
Yu, H., Li, T., Yu, W., Li, J., Huang, Y., Wang, L., & Liu, A. (2022). Regularized Graph Structure Learning with Semantic Knowledge for Multi-variates Time-Series Forecasting. In Proceedings of the 31st International Joint Conference on Artificial Intelligence, 2362–2368.
Zhou, H., Zhang, S., Peng, J., Zhang, S., Li, J., Xiong, H., & Zhang, W. (2021). Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting. In Proceedings of the 35th AAAI Conference on Artificial Intelligence, 35(12), 11106-11115.
Zhou, T., Ma, Z., Wen, Q., Wang, X., Sun, L., & Jin, R. (2022). FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting. In Proceedings of the International Conference on Machine Learning, 162, 27268-27286.
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