## 4 The Large-Scale Landslide Model Experiment and Bayesian Updating
### Surrogate Model  
Bayesian updating requires two sets of data: one of experimental data, and the other of simulation data. The experimental data were obtained through the above-mentioned large-scale landslide model experiment, and the data are shown in Figure 7. The simulation data were calculated according to the FEM in Section 4.2. It took 690 h (about 29 days) to perform a complete Bayesian update calculation with the FEM, and 2 h to use the surrogate model (Intel(R) Core(TM) i5-5200U CPU @ 2.20 GHz, RAM 8.00 GB). Therefore, a surrogate model was used in this study to obtain the simulation value. The surrogate model is a commonly used optimization method in engineering problems. When the actual problem is very computationally intensive and difficult to solve, a simplified model with less computational complexity and a rapid solution can be used to replace the original model to speed up the optimization process. In this study, an ANN was used to build the surrogate model. In order to improve the efficiency of Bayesian updating, we adopted the method of the surrogate model. We used an ANN to train the surrogate model. The ANN is an algorithm whose design is driven by the function of the human brain and its components. ANNs use nonlinear techniques, so they can be used to model highly complex and nonlinear systems. In this study, a fully connected feedforward multi-layer structure using a backpropagation momentum learning algorithm was adopted. This kind of ANN architecture usually consists of an input layer, some hidden layers, and an output layer. For us there were 10 neuron nodes used in each layer. Each node was interconnected to the nodes of the upper layer through adjustable weights, and horizontal, self-direction, or backward connection was not allowed. The calculation and expression ability of a single neuron is limited. However, when they are connected to each other, the entire network can model complex functions. The training pattern consists of a set of matched input and output vectors. The logical sigmoid function was used as the activation function. In order to develop the artificial neural network model, Neural Network Fitting toolbox and MATLAB R2019b were used. The Neural Network toolbox provides various parameters for neural network development, which can be selected flexibly. We set the distribution of the parameters of the SWCC model, and then used the SEEP/W software to calculate the value of the water content. We saved the SWCC model parameters and the generated water content data for the establishment of the surrogate model. The input data selected for this part were a array (2 \(\times\) 1000) of SWCC parameters \(a\) and \(n\), and the target array was water content data. In the training process, 70% of the data were used for training, 15% of the data for verification, and 15% of the data for testing. The training data were presented to the network during the training process, and the network was adjusted according to its errors. The verification data were used to measure the generalization of the network and stop training when the generalization stopped improving. The test data had no effect on training, so they provide an independent measurement of network performance during and after training. In this section, the number of hidden neurons was 10. Finally, we checked the error of the surrogate model built using an ANN. Figure 9 shows the regression diagram of the water content and SWCC parameters at specific points of the landslide model. In this figure, we can observe that all datasets were correctly fitted to the row. This shows that our neural network structure was correct, and it can also be used to predict the outputs of other input datasets. Figure 9a is the regression diagram of 70% of the training data. Figure 9b is the regression diagram of the 15% group of the validation data. Figure 9c is the regression diagram of the 15% group of test data. Figure 9d is the regression diagram of all data.