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

Yanling Li, Tianxing Dong, Yingying Shao and Xiaoming Mao ()
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Yanling Li: School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
Tianxing Dong: School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
Yingying Shao: School of Geosciences and Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450046, China
Xiaoming Mao: Ecological Environment Geo-Service Center of Henan Geological Bureau, Zhengzhou 450000, China

Sustainability, 2025, vol. 17, issue 18, 1-25

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.

Keywords: karst spring discharge; hydrological complexity; meta-heuristic optimization; feature mode decomposition; bidirectional gated recurrent unit Kolmogorov—Arnold networks (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2025
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