# Pore Water Pressure Prediction Based on Machine Learning Methods--Application to an Earth Dam Case
## 4 Results and Discussion
### Sensitivity Analysis  
The speed of convergence and expressive power of ML predictive models are affected not only by the architecture of the model but also by the choice of hyperparameters. In the case of the neural network series of ML, the architectural parameters are the number of hidden layers and the number of neurons in the hidden layers. The hyperparameters are learning rate, number of epochs, and number of samples (batch size) per learning. In this part, the GRU method is used to investigate the impacts of the hyperparameters in neural network architecture. These parameters are tunable and can directly affect how well a model performs. The values of hyperparameters are listed in Table 5; among them is the value, which is bolder and underlined, selected as the fixed value when one of the parameters changes, as shown in the variables. Every set of hyperparameters is validated 10 times. The batch size determines the number of samples that pass through the network during training. In an entire epoch, the overall N samples are divided into N/batch_size datasets. The learning is taken from the first dataset to the last one. Smaller batch sizes require less memory since the network is trained on fewer samples, reducing the overall memory demand during training. This is important, especially if the whole dataset is  
Figure 8: The distribution of the prediction PWP (testing set) and the residual contrast with the following measurements: (**a**) MLP (R\({}^{2}\) = 0.9947); (**b**) RF (R\({}^{2}\) = 0.9878); (**c**) GRU (R\({}^{2}\) = 0.9131); (**d**) RNNs (R\({}^{2}\) = 0.9213). The points represent the residual value, and the histogram on the right and top of the graph denotes the density of data. so enormous that it cannot be trained using an ordinary computer. Since the memory of the computer is always set as a power series of 2, the batch size is also defined as the same as the memory value. Figure 9a illustrates that the accuracy on testing datasets increases with smaller batch sizes, up until a batch size of 16, beyond which it sharply declines. Typically, networks are trained faster with mini-batches. This is because the networks update the weight after each propagation. Therefore, the batch size set of 16 is more efficient in modeling the PWP of this case study. The layers and neurons are seen as the basic model properties, which are determined by the model complexity. No hidden layers are needed if the data are regularly linearly distributed. For less complex data with fewer features, neural networks with one to two hidden layers are sufficient, as shown in Figure 9b. If data have large features, it will be necessary to use three to five hidden layers to obtain an optimum solution [13]. One or two hidden layers can be enough because the raw data have few features and reveal some kind of non-linear behavior. The larger the neurons, the more complicated the model. What stands out in Figure 9d is that 70 neurons are enough for the prediction of C2 PWP (when the number of neurons increases from 70 to 80, R2 becomes smaller). The learning rate stands out as a crucial hyperparameter in configuring neural networks. Choosing a proper learning rate is a delicate balance, as too small a value could lead to a lengthy training process with potential stagnation, while a value that is too large might result in rapid learning of sub-optimal weights or an unstable training process. Therefore, it is essential to examine the impact of the learning rate on model performance and gain  
Figure 9: Effect of different hyperparameters on the model prediction performance in GRU: (a) batch_size; (b) n_layers; (c) learning_rate; (d) n_neurons; (e) n_epochs. practical insights into how it influences the model's behavior. In this GRU model, the number of R\({}^{2}\) is likely to continue decreasing with the fall of the learning rate, as shown in Figure 9c. What can be clearly seen in this figure is that the R\({}^{2}\) rises to a high point and peaks when the learning rate equals 0.001.