Comparison of the efficacy of particle swarm optimization and stochastic gradient descent algorithms on multi-layer perceptron model to estimate longitudinal dispersion coefficients in natural streams

Accurate estimation of the longitudinal dispersion coefficient (LDC) is essential for modeling the pollution status in rivers. This research investigates the capabilities of machine-learning methods such as multi-layer perceptron (MLP), multi-layer perceptron trained with particle swarm optimization (MLP-PSO), multi-layer perceptron trained with Stochastic gradient descent deep learning (MLP-SGD) and different regressions including linear and non-linear regressions (LR and NLR) methods for determining the LDC of pollution in natural rivers and evaluates the accuracy of these methods in comparison with real measured data. Furthermore, the correlation coefficient (CC), root mean squared error (RMSE) and Willmott’s Index (WI) were implemented to evaluate the accuracies of the mentioned methods. Comparison of the results showed the superiority of the MLP-SGD model with CC of 0.923, RMSE of 281.4 and WI of 0.954, which indicates the undeniable accuracy and quality of the deep-learning model that can be used as a powerful model for LDC simulation. Also due to the acceptable performance of the PSO algorithm in the hybridization of the MLP model, the use of PSO algorithms is recommended to train machine-learning techniques for LDC estimation.