Uncertainty analysis of artificial neural network (ANN) and support vector machine (SVM) models in predicting monthly river flow (Case study: Ghezelozan River)

Introduction
River flow forecasting has been one of the important challenges of water resources management in recent decades, so many researchers have proposed different methods to improve the performance of forecasting models. In the last decade, artificial intelligence methods have been most widely used in the simulation of various processes, including hydrological processes, due to their flexibility and high accuracy in modeling. However, the results of these methods have always been associated with uncertainty due to several factors such as structure, algorithm, input data, and the type of method chosen for data calibration. One of the methods that can somewhat solve this problem is the uncertainty analysis of the predictions made by these models.
 
Materials and Methods
In this study, the uncertainty of the results of artificial neural network (ANN) and support vector machine (SVM) models in predicting the monthly flow of the river has been evaluated. In this research, the time series of the monthly flow of the Ghezelozan River using the data of the Bianlu-Yasaul Stream gauging station in 39 years from 1976 to 2014 was used, where 75% and 25% of the data was used for training and testing the models, respectively. In these models, to estimate the monthly flow of the Ghezelozan River, six different input combinations including the flow of one, two, and three months before and the number of months of the flow were used. Then, the accuracy and performance of the models were compared using the coefficient of determination (R) and root mean square of errors (RMSE). Finally, the uncertainty of the results of ANN and SVM models in predicting the monthly flow of the river was evaluated by the Monte-Carlo method using d-factor and 95PPU values.
 
Results and Discussion
The evaluation of the performance of the ANN model shows that the best performance is related to the combination where the flow of the previous two months and the number of the month of the flow are the inputs of the model so that R and RMSE indexes were obtained as 0.757 and 9.45, respectively. In the SVM model for the monthly river flow series, the best performance is related to the combination where the flow of one, two, and three months ago and the number of months of the flow were the inputs of the model, and the R and RMSE indexes for this input pattern were 0.729 and 10.946, respectively. After studying the uncertainty of the models, the results showed that the ANN model has more uncertainty in the output values compared to the SVM model, and this is while the d-factor of the ANN model, both in the training and test phase, it was more than the SVM model. The comparison of the uncertainty analysis of the results of the ANN and SVM models showed that the SVM model with d-factor and 95PPU values equal to 0.155 and 17.241, respectively, compared to the ANN model with d-factor and 95PPU values equal to 0.993 and 85.470, respectively, has less uncertainty in the output values. So the number of observation data placed in the 95% confidence range (95PPU) of the ANN model compared to the SVM model has increased significantly in both the training and testing phases. Also, the results showed that both models have more uncertainty in the months with a large volume of water, which can be due to the complexity of the process and the involvement of uncertain factors in these months, as well as the effect of factors that are not considered in the structure of predictive models.
Conclusion
The results of ANN and SVM models in predicting the monthly flow of the Ghezelozan River showed that although the ANN model with R-value equal to 0.757 and RMSE value equal to 9.45 has a good performance compared to the SVM model with R-value equal to 0.729 and RMSE value equal to 10.946 in predicting the river flow, the results of this model are associated with high uncertainty. The comparison of the uncertainty analysis of the results of ANN and SVM models by Monte-Carlo method showed that the SVM model with d-factor and 95PPU values equal to 0.155 and 17.241, respectively, compared to the ANN model with d-factor and 95PPU values equal to 0.993 and 85.470, respectively, has less uncertainty in predicting the monthly flow of the Ghezelozan River and it is better than ANN model. According to the results of this research, taking into account the fact that advanced artificial intelligence models also have uncertainty, it is necessary to apply these methods in the fields of risk management and future planning to obtain the best performance.