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The BPNN learning rate and momentum coefficient are found to be 0.01 and 0.95–1.0, respectively (Table 2). Reasonable model-field measurement matches (see below for a description of the model performance statistics) are obtained from the Hukou model after 3,000 iterations (Table 2). Hence, the same number of iterations is used for training other BPNN models, and convergence (based on MSE) to an optimal set of parameters was tested in each case. The closeness of the learning rate, momentum coefficient, and number of iterations for all models (and scenarios) demonstrates that the model results are not especially sensitive to these parameters. The number of neurons in the hidden layer is the main parameter that varies between models, ranging from 21 to 33 neurons to predict lake water levels with acceptable accuracy (Table 2). The sensitivity of the model to the optimal parameters in this study is consistent with previous BPNN modeling by Chen et al. (2012a, b), who found that the optimal number of nodes in the hidden layer was important for obtaining the best network architecture.

Table 2

Neural network parameters in BPNN models

Model parameters
BPNN modelModel scenarioLearning rateMomentum coefficientIteration numberInput nodesHidden nodes
Hukou S1 0.01 1.0 3,000 22 
S2 0.01 1.0 3,000 22 
S3 0.01 1.0 3,000 21 
Xingzi S1 0.01 1.0 3,000 28 
S2 0.01 1.0 3,000 25 
S3 0.01 1.0 3,000 25 
Duchang S1 0.01 0.98 3,000 22 
S2 0.01 0.98 3,000 22 
S3 0.01 0.98 3,000 21 
Tangyin S1 0.01 0.95 3,000 22 
S2 0.01 1.0 3,000 24 
S3 0.01 1.0 3,000 21 
Kangshan S1 0.01 0.98 3,000 22 
S2 0.01 0.98 3,000 33 
S3 0.01 0.98 3,000 23 
Model parameters
BPNN modelModel scenarioLearning rateMomentum coefficientIteration numberInput nodesHidden nodes
Hukou S1 0.01 1.0 3,000 22 
S2 0.01 1.0 3,000 22 
S3 0.01 1.0 3,000 21 
Xingzi S1 0.01 1.0 3,000 28 
S2 0.01 1.0 3,000 25 
S3 0.01 1.0 3,000 25 
Duchang S1 0.01 0.98 3,000 22 
S2 0.01 0.98 3,000 22 
S3 0.01 0.98 3,000 21 
Tangyin S1 0.01 0.95 3,000 22 
S2 0.01 1.0 3,000 24 
S3 0.01 1.0 3,000 21 
Kangshan S1 0.01 0.98 3,000 22 
S2 0.01 0.98 3,000 33 
S3 0.01 0.98 3,000 23 

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