{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T23:51:53Z","timestamp":1783036313383,"version":"3.54.6"},"reference-count":25,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T00:00:00Z","timestamp":1762128000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Young Talent fostering projects of North Minzu University","award":["2023QNPY08"],"award-info":[{"award-number":["2023QNPY08"]}]},{"DOI":"10.13039\/501100004772","name":"Natural Science Foundation of Ningxia","doi-asserted-by":"crossref","award":["2022AAC03287"],"award-info":[{"award-number":["2022AAC03287"]}],"id":[{"id":"10.13039\/501100004772","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Ningxia Basic Science Research Center of Mathematics","award":["2025NXSXZX0202"],"award-info":[{"award-number":["2025NXSXZX0202"]}]},{"name":"First-Class Disciplines Foundation of Ningxia","award":["NXYLXK2017B09"],"award-info":[{"award-number":["NXYLXK2017B09"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper proposes a hierarchical CNN-sLSTM-Attention model for long-sequence time series forecasting. It enhances efficiency by replacing traditional LSTMs with a stable LSTM (sLSTM) variant, which incorporates exponential gating and memory mixing. The architecture integrates CNN for local feature extraction, sLSTM blocks for temporal modeling, and an attention mechanism for dynamic weighting. This integrated design enables the effective processing of data with symmetric patterns or asymmetric patterns, which are prevalent in real-world time series. Experimental results on six datasets\u2014encompassing scenarios with symmetry\/asymmetry characteristics, such as temperature cycles and traffic flow fluctuations\u2014demonstrate the model\u2019s superior performance. Key findings include a 33% reduction in RMSE over standard LSTM on temperature prediction; 10\u00d7 faster convergence with stability achieved within 12 epochs for traffic flow prediction; a 15\u201347% reduction in long-sequence error attributable to the sLSTM component; and a 35% improvement in trend fitting due to the attention mechanism. Although the model outperforms baseline methods in handling periodic (often symmetric) and noisy data, its performance is limited on multimodal cases. These findings suggest that future work should focus on lightweight optimization, which has the potential to improve the model\u2019s adaptability to a broader spectrum of symmetry and asymmetry patterns in time series.<\/jats:p>","DOI":"10.3390\/sym17111846","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:55:22Z","timestamp":1762178122000},"page":"1846","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Comparative Study of CNN-sLSTM-Attention-Based Time Series Forecasting: Performance Evaluation on Data with Symmetry and Asymmetry Phenomena"],"prefix":"10.3390","volume":"17","author":[{"given":"Haopeng","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0746-3801","authenticated-orcid":false,"given":"Lufeng","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China"},{"name":"The Collaborative Innovation Center of Scientific Computing and Intelligent Information Processing, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,3]]},"reference":[{"key":"ref_1","first-page":"44","article-title":"Genetic algorithm optimized SVM model for transformer winding hotspot temperature prediction","volume":"29","author":"Chen","year":"2014","journal-title":"Trans. China Electrotech. Soc."},{"key":"ref_2","unstructured":"Hyndman, R.J., and Athanasopoulos, G. (2018). Forecasting: Principles and Practice, OTexts. [2nd ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2222","DOI":"10.1109\/TNNLS.2016.2582924","article-title":"LSTM: A Search Space Odyssey","volume":"28","author":"Greff","year":"2016","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhou, Z.K., Yang, L.C., and Wang, Z. (2022, January 28\u201330). Remaining Useful Life Prediction of AeroEngine using CNN-LSTM and mRMR Feature Selection. Proceedings of the 4th International Conference on System Reliability and Safety Engineering, Guangzhou, China.","DOI":"10.1109\/SRSE56746.2022.10067318"},{"key":"ref_5","unstructured":"Bahdanau, D., Cho, K., and Bengio, Y. (2015, January 7\u20139). Neural Machine Translation by Jointly Learning to Align and Translate. Proceedings of the International Conference on Learning Representations, San Diego, CA, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3530811","article-title":"Efficient Transformers: A Survey","volume":"55","author":"Tay","year":"2022","journal-title":"ACM Comput. Surv."},{"key":"ref_7","unstructured":"Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, \u0141., and Polosukhin, I. (2017). Attention is All You Need. Advances in Neural Information Processing Systems 30, Curran Associates, Inc."},{"key":"ref_8","unstructured":"Nie, Y., Nguyen, N.H., Sinthong, P., and Kalagnanam, J. (2023, January 1\u20135). A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. Proceedings of the International Conference on Learning Representations, Kigali, Rwanda."},{"key":"ref_9","unstructured":"Liu, Y., Hu, T., Zhang, H., Wu, H., Wang, S., Ma, L., and Long, M. (2023). iTransformer: Inverted Transformers Are Effective for Time Series Forecasting. arXiv."},{"key":"ref_10","unstructured":"Wu, H., Hu, T., Liu, Y., Zhou, H., Wang, J., and Long, M. (2023, January 1\u20135). TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis. Proceedings of the 11th International Conference on Learning Representations, Kigali, Rwanda."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhou, Z.H. (2021). Machine Learning, Springer.","DOI":"10.1007\/978-981-15-1967-3"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_13","unstructured":"Zhang, S., Wu, Y., Che, T., Lin, Z., Memisevic, R., Salakhutdinov, R.R., and Bengio, Y. (2016). Architectural complexity measures of recurrent neural networks. Advances in Neural Information Processing Systems 29, Curran Associates, Inc."},{"key":"ref_14","first-page":"5528714","article-title":"Pan-Denoising: Guided Hyperspectral Image Denoising via Weighted Represent Coefficient Total Variation","volume":"62","author":"Xu","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5545214","DOI":"10.1109\/TGRS.2022.3227735","article-title":"Hyperspectral Image Denoising by Asymmetric Noise Modeling","volume":"60","author":"Xu","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Xu, S., Zhao, Z., Cao, X., Peng, J., Zhao, X., Meng, D., Zhang, Y., Timofte, R., and Gool, L.V. (2025). Parameterized Low-Rank Regularizer for High-dimensional Visual Data. Int. J. Comput. Vis.","DOI":"10.1007\/s11263-025-02569-2"},{"key":"ref_17","unstructured":"Han, S., Mao, H., and Dally, W.J. (2016, January 2\u20134). Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding. Proceedings of the 4th International Conference on Learning Representations, ICLR 2016, San Juan, Puerto Rico."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep Learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"ref_19","unstructured":"Beck, M., P\u00f6ppel, K., Spanring, M., Auer, T., Prudnikova, O., Kopp, M., Klbl, G., Brandstetter, J., and Hochreiter, S. (2024). xLSTM: Extended Long Short-Term Memory. arXiv."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"20200209","DOI":"10.1098\/rsta.2020.0209","article-title":"Time Series Forecasting with Deep Learning: A Survey","volume":"379","author":"Lim","year":"2021","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Orr, G.B., and M\u00fcller, K.R. (1998). Early Stopping\u2014But When. Neural Networks: Tricks of the Trade, Springer.","DOI":"10.1007\/3-540-49430-8"},{"key":"ref_22","unstructured":"Kong, Y., Wang, Z., Nie, Y., Zhang, Q., and Li, D. (2025, January 22\u201327). Unlocking the Power of LSTM for Long Term Time Series Forecasting. Proceedings of the AAAI Conference on Artificial Intelligence, Vancouver, BC, Canada."},{"key":"ref_23","first-page":"1929","article-title":"Dropout: A Simple Way to Prevent Neural Networks from Overfitting","volume":"15","author":"Srivastava","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Mariappan, Y., Ramasamy, K., and Velusamy, D. (2025). An Optimized Deep Learning Based Hybrid Model for Prediction of Daily Average Global Solar Irradiance Using CNN-SLSTM Architecture. Sci. Rep., 15.","DOI":"10.1038\/s41598-025-95118-3"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"23498","DOI":"10.1109\/JSEN.2021.3109623","article-title":"A Novel Cap-LSTM Model for Remaining Useful Life Prediction","volume":"21","author":"Zhao","year":"2021","journal-title":"IEEE Sens. J."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1846\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T05:12:50Z","timestamp":1762319570000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1846"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,3]]},"references-count":25,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["sym17111846"],"URL":"https:\/\/doi.org\/10.3390\/sym17111846","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,3]]}}}