Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise forecasting of river’s streamflow - Amin Gharehbaghi; Redvan Ghasemlounia; Farshad Ahmadi; Rasoul Mirabbasi; Ali Torabi Haghighi (Scientific Reports)
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.