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.