Hybrid Deep Learning Combining Mode Decomposition and Intelligent Optimization for Discharge Forecasting: A Case Study of the Baiquan Karst Spring

Karst springs play a critical strategic role in regional economic and ecological sustainability, yet their spatiotemporal heterogeneity and hydrological complexity pose substantial challenges for flow prediction. This study proposes FMD-mGTO-BiGRU-KAN, a four-stage hybrid deep learning architecture...

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Veröffentlicht in:	Sustainability Jg. 17; H. 18; S. 8101
Hauptverfasser:	Li, Yanling, Dong, Tianxing, Shao, Yingying, Mao, Xiaoming
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Basel MDPI AG 01.09.2025
Schlagworte:	Aquifers Case studies Decomposition method Deep learning Environmental aspects Fault lines Geology Groundwater Hydrology Karst Machine learning Mathematical optimization Natural history Optimization algorithms Prediction theory Springs Stream measurements Stress concentration Technology application Time series China
ISSN:	2071-1050, 2071-1050
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Abstract	Karst springs play a critical strategic role in regional economic and ecological sustainability, yet their spatiotemporal heterogeneity and hydrological complexity pose substantial challenges for flow prediction. This study proposes FMD-mGTO-BiGRU-KAN, a four-stage hybrid deep learning architecture for daily spring flow prediction that integrates multi-feature signal decomposition, meta-heuristic optimization, and interpretable neural network design: constructing an Feature Mode Decomposition (FMD) decomposition layer to mitigate modal aliasing in meteorological signals; employing the improved Gorilla Troops Optimizer (mGTO) optimization algorithm to enable autonomous hyperparameter evolution, overcoming the limitations of traditional grid search; designing a Bidirectional Gated Recurrent Unit (BiGRU) network to capture long-term historical dependencies in spring flow sequences through bidirectional recurrent mechanisms; introducing Kolmogorov–Arnold Networks (KAN) to replace the fully connected layer, and improving the model interpretability through differentiable symbolic operations; Additionally, residual modules and dropout blocks are incorporated to enhance generalization capability, reduce overfitting risks. By integrating multiple deep learning algorithms, this hybrid model leverages their respective strengths to adeptly accommodate intricate meteorological conditions, thereby enhancing its capacity to discern the underlying patterns within complex and dynamic input features. Comparative results against benchmark models (LSTM, GRU, and Transformer) show that the proposed framework achieves 82.47% and 50.15% reductions in MSE and RMSE, respectively, with the NSE increasing by 8.01% to 0.9862. The prediction errors are more tightly distributed, and the proposed model surpasses the benchmark model in overall performance, validating its superiority. The model’s exceptional prediction ability offers a novel high-precision solution for spring flow prediction in complex hydrological systems.
AbstractList	Karst springs play a critical strategic role in regional economic and ecological sustainability, yet their spatiotemporal heterogeneity and hydrological complexity pose substantial challenges for flow prediction. This study proposes FMD-mGTO-BiGRU-KAN, a four-stage hybrid deep learning architecture for daily spring flow prediction that integrates multi-feature signal decomposition, meta-heuristic optimization, and interpretable neural network design: constructing an Feature Mode Decomposition (FMD) decomposition layer to mitigate modal aliasing in meteorological signals; employing the improved Gorilla Troops Optimizer (mGTO) optimization algorithm to enable autonomous hyperparameter evolution, overcoming the limitations of traditional grid search; designing a Bidirectional Gated Recurrent Unit (BiGRU) network to capture long-term historical dependencies in spring flow sequences through bidirectional recurrent mechanisms; introducing Kolmogorov–Arnold Networks (KAN) to replace the fully connected layer, and improving the model interpretability through differentiable symbolic operations; Additionally, residual modules and dropout blocks are incorporated to enhance generalization capability, reduce overfitting risks. By integrating multiple deep learning algorithms, this hybrid model leverages their respective strengths to adeptly accommodate intricate meteorological conditions, thereby enhancing its capacity to discern the underlying patterns within complex and dynamic input features. Comparative results against benchmark models (LSTM, GRU, and Transformer) show that the proposed framework achieves 82.47% and 50.15% reductions in MSE and RMSE, respectively, with the NSE increasing by 8.01% to 0.9862. The prediction errors are more tightly distributed, and the proposed model surpasses the benchmark model in overall performance, validating its superiority. The model’s exceptional prediction ability offers a novel high-precision solution for spring flow prediction in complex hydrological systems.
Audience	Academic
Author	Shao, Yingying Dong, Tianxing Mao, Xiaoming Li, Yanling
Author_xml	– sequence: 1 givenname: Yanling surname: Li fullname: Li, Yanling – sequence: 2 givenname: Tianxing surname: Dong fullname: Dong, Tianxing – sequence: 3 givenname: Yingying surname: Shao fullname: Shao, Yingying – sequence: 4 givenname: Xiaoming surname: Mao fullname: Mao, Xiaoming
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Cites_doi	10.1016/j.jhydrol.2024.132235 10.1016/j.jhydrol.2022.127511 10.1002/2013RG000443 10.1016/j.knosys.2023.110462 10.1002/int.22535 10.1016/j.scitotenv.2018.06.184 10.1109/ETFG55873.2023.10407702 10.3115/v1/D14-1179 10.3390/w13182540 10.1109/ACCESS.2022.3186519 10.1007/s10462-024-10838-8 10.1007/s10040-013-1046-4 10.1007/s10040-004-0402-9 10.3390/en18010106 10.1007/978-1-4614-4106-9 10.1016/j.jhydrol.2022.127907 10.1007/s43832-022-00015-9 10.1029/2022WR032602 10.1109/CVPR.2016.90 10.1109/TIE.2022.3156156 10.1155/2018/8328167 10.1007/s10462-021-09992-0 10.1016/j.jhydrol.2024.130946 10.5194/hess-12-989-2008 10.1016/j.jhydrol.2020.125423 10.1007/s11269-014-0527-0 10.1007/s10040-020-02139-5 10.1002/2016WR018850 10.1109/TNNLS.2016.2582924 10.1016/j.jhydrol.2022.128116 10.1109/ACCESS.2019.2900371 10.1007/s11269-014-0898-2 10.1016/j.jhydrol.2024.131128 10.1002/9781119079231 10.1007/978-1-4020-5729-8_4 10.1016/j.jhydrol.2020.125320 10.1007/s00366-021-01368-w
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SubjectTerms	Aquifers Case studies Decomposition method Deep learning Environmental aspects Fault lines Geology Groundwater Hydrology Karst Machine learning Mathematical optimization Natural history Optimization algorithms Prediction theory Springs Stream measurements Stress concentration Technology application Time series
Title	Hybrid Deep Learning Combining Mode Decomposition and Intelligent Optimization for Discharge Forecasting: A Case Study of the Baiquan Karst Spring
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