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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Bibliographic Details
Published in:Sustainability Vol. 17; no. 18; p. 8101
Main Authors: Li, Yanling, Dong, Tianxing, Shao, Yingying, Mao, Xiaoming
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.09.2025
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:2071-1050
2071-1050
DOI:10.3390/su17188101