Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river's streamflow
Gharehbaghi, Amin; Ghasemlounia, Redvan; Ahmadi, Farshad; Mirabbassi, Rasoul; Torabi Haghighi, Ali (2025-06-03)
Springer
03.06.2025
Gharehbaghi, A., Ghasemlounia, R., Ahmadi, F. et al. Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river’s streamflow. Sci Rep 15, 19436 (2025). https://doi.org/10.1038/s41598-025-03185-3
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https://creativecommons.org/licenses/by-nc-nd/4.0/
© The Author(s) 2025. This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
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Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202506064177
https://urn.fi/URN:NBN:fi:oulu-202506064177
Tiivistelmä
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 (CCRSFm) in Iran. The Pearson’s correlation coefficient (PCC) and Cosine Amplitude Sensitivity (CAS) as feature (input) selection process determine the only precipitation (Pm) 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 R2 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 R2 by 6.8% and reduce in the value of RMSE by 20.4%. Comparatively, standard individual GRU and Bi-GRU models result in an R2 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.
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 (CCRSFm) in Iran. The Pearson’s correlation coefficient (PCC) and Cosine Amplitude Sensitivity (CAS) as feature (input) selection process determine the only precipitation (Pm) 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 R2 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 R2 by 6.8% and reduce in the value of RMSE by 20.4%. Comparatively, standard individual GRU and Bi-GRU models result in an R2 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.
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