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Fig. 2. (a) unit hydrograph and precipitation through the research time frame, (b) Thiessen polygons and each piezometer weight, and (c) Temperature (C) and evaporation (mm) values during research time frame In this investigation, we employed models based on Al in addition to the numerical model developed by GMS in order to forecast changes in the level of groundwater in the plain. This was done to reduce the amount of time spent processing vast volumes of data and save time overall, in addition to taking into consideration the complexity of mathematical models. The hydrograph of the plain groundwater unit that was derived from a 12-piezometer water level data set during a 198-month statistical

Figure 2 (a) unit hydrograph and precipitation through the research time frame, (b) Thiessen polygons and each piezometer weight, and (c) Temperature (C) and evaporation (mm) values during research time frame In this investigation, we employed models based on Al in addition to the numerical model developed by GMS in order to forecast changes in the level of groundwater in the plain. This was done to reduce the amount of time spent processing vast volumes of data and save time overall, in addition to taking into consideration the complexity of mathematical models. The hydrograph of the plain groundwater unit that was derived from a 12-piezometer water level data set during a 198-month statistical

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ABSTRACT ’Department of Civil Engineering, Faculty of Engineering, Razi University, Kermanshah, Iran. ?Department of Water Engineering, Faculty of Agricultural Science and Engineering, Razi University, Kermanshah, Irar
ABSTRACT ’Department of Civil Engineering, Faculty of Engineering, Razi University, Kermanshah, Iran. ?Department of Water Engineering, Faculty of Agricultural Science and Engineering, Razi University, Kermanshah, Irar
Fig. 1. Study area geographical situation for numerical and Al modeling. It's possible that the model's assumptions are vastly underestimated when compared to the real-world system's complexity and performance. Oversimplifying the system under examination could impede us from gleaning important data (Beear. 2010).Therefore, it seems necessary to convert to more complicated techniques, such as numerical methods and mathematical models, from more basic ones that use less data but still generate accurate results (Haafezparast and Maarabi. 2021a; Hafezparast and Marabi. 2021b; Faatemi and Paarvini. 2022). Stochastic approaches and Al have been incorporated in some of these models (Moeini et al. 2017a, 2017b; Malekpor and Tabbari, 2020). Although these strategies require less time and are more reliable at forecasting groundwater changes, they often depend on a series of means rather than simulation models to generate predictions regarding GWLs (Guzzman et al.2019; Nadiiri et al.2019).
Fig. 1. Study area geographical situation for numerical and Al modeling. It's possible that the model's assumptions are vastly underestimated when compared to the real-world system's complexity and performance. Oversimplifying the system under examination could impede us from gleaning important data (Beear. 2010).Therefore, it seems necessary to convert to more complicated techniques, such as numerical methods and mathematical models, from more basic ones that use less data but still generate accurate results (Haafezparast and Maarabi. 2021a; Hafezparast and Marabi. 2021b; Faatemi and Paarvini. 2022). Stochastic approaches and Al have been incorporated in some of these models (Moeini et al. 2017a, 2017b; Malekpor and Tabbari, 2020). Although these strategies require less time and are more reliable at forecasting groundwater changes, they often depend on a series of means rather than simulation models to generate predictions regarding GWLs (Guzzman et al.2019; Nadiiri et al.2019).
owns the lowest number of simulation mistakes possible is shown in this image. The standard deviation, correlation coefficient and root- mean-squared error value are the three indicators used.
owns the lowest number of simulation mistakes possible is shown in this image. The standard deviation, correlation coefficient and root- mean-squared error value are the three indicators used.
The following equation may be used to compute the AF of hidden layer neurons (HLNs) for every learning sample in an ELM network with the following parameters: the number of "j" neurons in the hidden layer; the number of "i" input neurons; and the number of "k" learning samples. H, => (W,X,)+B, (7) here, =, 4,50 =Dy,... bp 3X = XX, and Bis the weight vector between the HLNs andH’ is the hidden and quasi-inverted layer of Moore-Penrose H matrix. T is the vector of correlations between training sample weights. From the descriptions, we may infer that there are two stages of ELM instruction. The first involves computing the output of the hidden layer H matrix by randomly assigning weights and biases to HLNs; the second involves computing the output weight using the quasi-inverse Moore-Penrose H matrix and goal values for various training samples. Finding the H matrix for the hidden layer takes less time than using traditional iteration-based methods like Levenberg- Marquardt, which don't use nonlinear optimization techniques. As a result, it takes much less time to train a network (Huang, Zhu, and Siew, 2006). Machine designed for extreme learning by Huang et al. (2004, 2006) and dubbed ELM. ELM uses a random specification of input weights and an analytical determination of output weights. The outline of this method is seen in Fig. 2a. ELM does not employ bias for output neurons like a single layer feed forward neural network (SLFFNN). Each neuron in the hidden layer is linked to every neuron in the input layer.Neurons in the hidden layer have activation functions (AF) that are piecewise continuous, while those in the output layer have AFs that are linear. ELM drastically shortens the time needed to train a network by employing a number of distinct algorithms to compute weights and biases. With n hidden nodes, SLFFNN can be mathematically described as:
The following equation may be used to compute the AF of hidden layer neurons (HLNs) for every learning sample in an ELM network with the following parameters: the number of "j" neurons in the hidden layer; the number of "i" input neurons; and the number of "k" learning samples. H, => (W,X,)+B, (7) here, =, 4,50 =Dy,... bp 3X = XX, and Bis the weight vector between the HLNs andH’ is the hidden and quasi-inverted layer of Moore-Penrose H matrix. T is the vector of correlations between training sample weights. From the descriptions, we may infer that there are two stages of ELM instruction. The first involves computing the output of the hidden layer H matrix by randomly assigning weights and biases to HLNs; the second involves computing the output weight using the quasi-inverse Moore-Penrose H matrix and goal values for various training samples. Finding the H matrix for the hidden layer takes less time than using traditional iteration-based methods like Levenberg- Marquardt, which don't use nonlinear optimization techniques. As a result, it takes much less time to train a network (Huang, Zhu, and Siew, 2006). Machine designed for extreme learning by Huang et al. (2004, 2006) and dubbed ELM. ELM uses a random specification of input weights and an analytical determination of output weights. The outline of this method is seen in Fig. 2a. ELM does not employ bias for output neurons like a single layer feed forward neural network (SLFFNN). Each neuron in the hidden layer is linked to every neuron in the input layer.Neurons in the hidden layer have activation functions (AF) that are piecewise continuous, while those in the output layer have AFs that are linear. ELM drastically shortens the time needed to train a network by employing a number of distinct algorithms to compute weights and biases. With n hidden nodes, SLFFNN can be mathematically described as:
Fig. 4. Numerical model components prepared and plain GWL in steady state. In this regard, the multilayer perceptron (MLP) model is also one of the methods that is most widely applicable. The input, whichever hidder layer(s) are present, and the output are the three layers that togethe compose an MLP. Each neuron in one layer is directly linked to every neuron in the layer above it in the layered architecture of the brain. It is possible to train multilayer neural networks to solve problems that are nonlinear and/or involve many decisions. In neural networks, if there are m features in the data set, there will be m neurons in the input layer and the inputs will need to be multiplied by n up to the weight of W. | there are n features in the data set, then there will be n neurons in the output layer. Additional characteristics of the data set have the potentia fo have an effect on the output, also known as the dependent variable Given that there are n neurons in the hidden layer, you will require r sets of weights (W1, W2,..., Wn) in order to perform the operation o multiplying the weights by X inputs. It is not possible to accurately predict the model's output without first correcting and optimizing the weights in each layer. There are many different approaches to traininc 3.2. Prediction of groundwater level based on artificial intelligence
Fig. 4. Numerical model components prepared and plain GWL in steady state. In this regard, the multilayer perceptron (MLP) model is also one of the methods that is most widely applicable. The input, whichever hidder layer(s) are present, and the output are the three layers that togethe compose an MLP. Each neuron in one layer is directly linked to every neuron in the layer above it in the layered architecture of the brain. It is possible to train multilayer neural networks to solve problems that are nonlinear and/or involve many decisions. In neural networks, if there are m features in the data set, there will be m neurons in the input layer and the inputs will need to be multiplied by n up to the weight of W. | there are n features in the data set, then there will be n neurons in the output layer. Additional characteristics of the data set have the potentia fo have an effect on the output, also known as the dependent variable Given that there are n neurons in the hidden layer, you will require r sets of weights (W1, W2,..., Wn) in order to perform the operation o multiplying the weights by X inputs. It is not possible to accurately predict the model's output without first correcting and optimizing the weights in each layer. There are many different approaches to traininc 3.2. Prediction of groundwater level based on artificial intelligence
The accuracy of such models was examined based on their RMSE, NRMSE, NASH, and R values in order to forecast future GWL changes n the Lur plain. These data were not employed for modeling and were »xcluded during the first investigation since there was not a significant association between the data on air temperature and evaporation anc he data on GWL. Consequently, these data were not used. \dditionally, the incorporation of precipitation data into the models as nput data resulted in a reduction in the accuracy of the models yredictions. As a result, there was no incorporation of precipitation data nto any of the leading models. Table 1 presents the results that each »f these models performed the best in when they were put through thei aces. According to the data shown in this table, ORELM demonstrates Superior accuracy than other models both during the training and testin¢ stages across the board. Therefore, the ELM model comes in at numbe: two in terms of the accuracy of its predictions.Figure 6 depicts the sparsity of points around the line Y = X as well as the square of the correlation coefficient for the purpose of selecting the optimal Al mode during the modeling test phase for each GA-ANN, ICA-ANN, ELM ORELM, and GMDH model. This information is shown for each of the models. The fact that points in the ORELM model are distributed in < more regular pattern and are located closer to one another around the ine Y = X is another indication that this model is more precise thar others.
The accuracy of such models was examined based on their RMSE, NRMSE, NASH, and R values in order to forecast future GWL changes n the Lur plain. These data were not employed for modeling and were »xcluded during the first investigation since there was not a significant association between the data on air temperature and evaporation anc he data on GWL. Consequently, these data were not used. \dditionally, the incorporation of precipitation data into the models as nput data resulted in a reduction in the accuracy of the models yredictions. As a result, there was no incorporation of precipitation data nto any of the leading models. Table 1 presents the results that each »f these models performed the best in when they were put through thei aces. According to the data shown in this table, ORELM demonstrates Superior accuracy than other models both during the training and testin¢ stages across the board. Therefore, the ELM model comes in at numbe: two in terms of the accuracy of its predictions.Figure 6 depicts the sparsity of points around the line Y = X as well as the square of the correlation coefficient for the purpose of selecting the optimal Al mode during the modeling test phase for each GA-ANN, ICA-ANN, ELM ORELM, and GMDH model. This information is shown for each of the models. The fact that points in the ORELM model are distributed in < more regular pattern and are located closer to one another around the ine Y = X is another indication that this model is more precise thar others.
With the help of a Taylor diagram, we were able to select the best possible model with complete assurance. Figure 8 is a representation of a Taylor diagram (Taylor, 2001) that can be used to determine which of the GA-ANN, ICA-ANN, ELM, ORELM, and GMDH approaches is the most accurate at predicting the plain GWL. The centered RMSE has a proportional relationship with the distance that separates the point that was generated and the point that was observed. According to the findings of a study that was conducted by Zeynoddin and colleagues (2018), the model that is the most accurate representation of the data is the one in which the simulated data have a coefficient of determination of 1 and a standard deviation that is relatively close to the values that were actually observed. The observations of the GWL are represented by point A, and the assessment results of the models discussed earlier are displayed by points B through F. The correlation
With the help of a Taylor diagram, we were able to select the best possible model with complete assurance. Figure 8 is a representation of a Taylor diagram (Taylor, 2001) that can be used to determine which of the GA-ANN, ICA-ANN, ELM, ORELM, and GMDH approaches is the most accurate at predicting the plain GWL. The centered RMSE has a proportional relationship with the distance that separates the point that was generated and the point that was observed. According to the findings of a study that was conducted by Zeynoddin and colleagues (2018), the model that is the most accurate representation of the data is the one in which the simulated data have a coefficient of determination of 1 and a standard deviation that is relatively close to the values that were actually observed. The observations of the GWL are represented by point A, and the assessment results of the models discussed earlier are displayed by points B through F. The correlation
g. 6. At the stage of the modeling test when Al models are being evaluated, a graphical depiction of the sparsity of points near the line Y = X and the square of the correlation coefficient for models (a) GA-ANN (b) ICA-ANN (c) ELM (d) ORELM and (e) GMDH.
g. 6. At the stage of the modeling test when Al models are being evaluated, a graphical depiction of the sparsity of points near the line Y = X and the square of the correlation coefficient for models (a) GA-ANN (b) ICA-ANN (c) ELM (d) ORELM and (e) GMDH.
Fig. 8. At the stage of the modeling test, the Taylor graphic diagram is used to choose the most effective Al model Fig. 7. (a) Time series of observed and (b) predicted groundwater level, and (c) MSE error index and distribution of errors for train stage, (d) time series of observed and (e) predicted groundwater level, and (f) MSE error index and distribution of errors for test stage based on the best model (ORELM).
Fig. 8. At the stage of the modeling test, the Taylor graphic diagram is used to choose the most effective Al model Fig. 7. (a) Time series of observed and (b) predicted groundwater level, and (c) MSE error index and distribution of errors for train stage, (d) time series of observed and (e) predicted groundwater level, and (f) MSE error index and distribution of errors for test stage based on the best model (ORELM).
Related topics:
Hybrid ModelsGroundwater level prediction
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