3.4. ANN-Optimization model
ANN is a widely used technique to map non-linear and black box functions for fast evaluations. Feed Forward Neural Network (FFNN) is the most commonly used ANN. It consists of multiple parallel layers of memory units (neurons). Each layer of neuron is fully connected with its adjacent layer and the strength of the connection is defined as its weight. The backpropagation technique is used to find these weights such that error between the actual and predicted values, is minimized.
For this work, nearly 104 random data points, with zone-wise discharge as input and leakage out (L with penalty) and total discharge (Q with penalty) as output, were generated using a calibrated groundwater simulation model. The total data is divided into three subsets: training (70%), validation (15%), and testing (15%). An FFNN with a single hidden layer and enough hidden layer size (neurons) is capable of any input-output mapping (The MathWork Inc.). But the ANN training time also increases with an increase in the size of the training dataset and layer size (neurons). This makes the combination of large training data set and layer size infeasible. Different layer sizes (20, 10, 25) were tested and the best of the ANN model was selected based on R-square and Mean Absolute Percentage Error (MAPE) of Leakage out because the total discharge predictions were accurate. Along with these matrices, the values of Maximum Absolute Error (MXAE) and Root Mean Squared Error (RMSE) are shown in Table 3.
As is evident from the table, the “Model 2”, under leakage out, is having a good R-square value (near to 0.97) and a high MAPE value (near to 25%). This means that even though the actual and predicted output are correlated, there is a significant deviation existing from the actual model. Even if the optimum points for Model 2 (ANN) are derived using evolutionary algorithms, the correct value of decision variables could not be obtained. It makes the use of this ANN model unsuitable for the optimization model for Model 2. Thus, final optimization using ANN is performed for “Model 1” and “Model 3” only.