Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river’s streamflow
Abstract Streamflow contemplates a fundamental criterion to evaluate the impact of human activities and climate changes on the hydrological cycle. In this study, a novel innovative deep neural network (DNN) structure by integrating a double Gated Recurrent Units (GRU) neural network model with a mul...
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Nature Portfolio
2025-06-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-03185-3 |
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| author | Amin Gharehbaghi Redvan Ghasemlounia Farshad Ahmadi Rasoul Mirabbasi Ali Torabi Haghighi |
| author_facet | Amin Gharehbaghi Redvan Ghasemlounia Farshad Ahmadi Rasoul Mirabbasi Ali Torabi Haghighi |
| author_sort | Amin Gharehbaghi |
| collection | DOAJ |
| description | Abstract Streamflow contemplates a fundamental criterion to evaluate the impact of human activities and climate changes on the hydrological cycle. In this study, a novel innovative deep neural network (DNN) structure by integrating a double Gated Recurrent Units (GRU) neural network model with a multiplication layer and meta-heuristic whale optimization algorithm (WOA) (i.e., hybrid 2GRU×–WOA model) is developed to improve the prediction accuracy and performance of mean monthly Chehel-Chai River’s streamflow (CCRSF m ) in Iran. The Pearson’s correlation coefficient (PCC) and Cosine Amplitude Sensitivity (CAS) as feature (input) selection process determine the only precipitation (P m ) as the most effective input variable among a list of on-site potential climate time series parameters recorded in the study area. Thanks to a well-proportioned layer network structural framework in the suggested hybrid 2GRU×–WOA model, it leads to an appropriate total learnable parameter (TLP) compared to standard individual GRU and Bi-GRU as the benchmark models developed in the comparable meta-parameters. This hybrid model under the optimal meant meta-parameters tuned i.e., coupling a state activation functions (SAF) of tanh-softsign, dropout rate (P-rate) of 0.5, numbers of hidden neurons (NHN) of 70, outperforms with an R 2 of 0.79, NSE of 0.76, MAE of 0.21 (m3/s), MBE of -0.11(m3/s), and RMSE of 0.36 (m3/s). Hybridizing the 2GRU× model with WOA algorithm causes to increase in the value of R 2 by 6.8% and reduce in the value of RMSE by 20.4%. Comparatively, standard individual GRU and Bi-GRU models result in an R 2 of 0.59 and 0.66, NSE of 0.55 and 0.6, MAE of 0.91 and 0.53 (m3/s), MBE of 0.047 and − 0.06 (m3/s), RMSE of 1.29 and 0.83 (m3/s), respectively. |
| format | Article |
| id | doaj-art-d2cd9566e04f4e95a04398ffa347316c |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Nature Portfolio |
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| series | Scientific Reports |
| spelling | doaj-art-d2cd9566e04f4e95a04398ffa347316c2025-08-20T03:46:01ZengNature PortfolioScientific Reports2045-23222025-06-0115112010.1038/s41598-025-03185-3Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river’s streamflowAmin Gharehbaghi0Redvan Ghasemlounia1Farshad Ahmadi2Rasoul Mirabbasi3Ali Torabi Haghighi4Department of Civil Engineering, Faculty of Engineering, Hasan Kalyoncu UniversityDepartment of Civil Engineering, Faculty of Engineering, Istanbul Gedik UniversityDepartment of Hydrology & Water Resources Engineering, Shahid Chamran University of AhvazDepartment of Water Engineering, Shahrekord UniversityWater, Energy, and Environmental Engineering Research Unit, University of OuluAbstract Streamflow contemplates a fundamental criterion to evaluate the impact of human activities and climate changes on the hydrological cycle. In this study, a novel innovative deep neural network (DNN) structure by integrating a double Gated Recurrent Units (GRU) neural network model with a multiplication layer and meta-heuristic whale optimization algorithm (WOA) (i.e., hybrid 2GRU×–WOA model) is developed to improve the prediction accuracy and performance of mean monthly Chehel-Chai River’s streamflow (CCRSF m ) in Iran. The Pearson’s correlation coefficient (PCC) and Cosine Amplitude Sensitivity (CAS) as feature (input) selection process determine the only precipitation (P m ) as the most effective input variable among a list of on-site potential climate time series parameters recorded in the study area. Thanks to a well-proportioned layer network structural framework in the suggested hybrid 2GRU×–WOA model, it leads to an appropriate total learnable parameter (TLP) compared to standard individual GRU and Bi-GRU as the benchmark models developed in the comparable meta-parameters. This hybrid model under the optimal meant meta-parameters tuned i.e., coupling a state activation functions (SAF) of tanh-softsign, dropout rate (P-rate) of 0.5, numbers of hidden neurons (NHN) of 70, outperforms with an R 2 of 0.79, NSE of 0.76, MAE of 0.21 (m3/s), MBE of -0.11(m3/s), and RMSE of 0.36 (m3/s). Hybridizing the 2GRU× model with WOA algorithm causes to increase in the value of R 2 by 6.8% and reduce in the value of RMSE by 20.4%. Comparatively, standard individual GRU and Bi-GRU models result in an R 2 of 0.59 and 0.66, NSE of 0.55 and 0.6, MAE of 0.91 and 0.53 (m3/s), MBE of 0.047 and − 0.06 (m3/s), RMSE of 1.29 and 0.83 (m3/s), respectively.https://doi.org/10.1038/s41598-025-03185-3GRU and Bi-GRU modelsMeta-heuristic Whale optimization algorithmNovel hybrid 2GRU×–WOA modelTLP parameterChehel-Chai river’s streamflow |
| spellingShingle | Amin Gharehbaghi Redvan Ghasemlounia Farshad Ahmadi Rasoul Mirabbasi Ali Torabi Haghighi Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river’s streamflow Scientific Reports GRU and Bi-GRU models Meta-heuristic Whale optimization algorithm Novel hybrid 2GRU×–WOA model TLP parameter Chehel-Chai river’s streamflow |
| title | Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river’s streamflow |
| title_full | Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river’s streamflow |
| title_fullStr | Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river’s streamflow |
| title_full_unstemmed | Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river’s streamflow |
| title_short | Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river’s streamflow |
| title_sort | developing a novel hybrid model based on gru deep neural network and whale optimization algorithm for precise forecasting of river s streamflow |
| topic | GRU and Bi-GRU models Meta-heuristic Whale optimization algorithm Novel hybrid 2GRU×–WOA model TLP parameter Chehel-Chai river’s streamflow |
| url | https://doi.org/10.1038/s41598-025-03185-3 |
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