## 5 Model Evaluation
### Deep Learning Models  
The deep learning models DNN and ResNet are used to establish the shear strength prediction model of RCSW, the hyperparameters are optimized by calling the 'tuner.search' method, the training set is used for training, and the optimized parameter values are shown in Table 6. For the DNN model, the optimal number of layers is four, which takes into account the model complexity and training difficulty. The units' number in each layer is 256, 256, 96, and 32, showing that the first two layers can effectively capture complex features, while the gradual reduction in the number of units in the subsequent layers is in line with the principle of layer-by-layer abstraction in deep learning. In addition, the first and third layers use the ReLU activation function, while the second and fourth layers use the Sigmoid and ReLU, respectively, demonstrating effective modeling of nonlinear relationships. The optimizer is chosen to be Adam, which is recognized for its superiority in handling sparse data and convergence speed. For the ResNet model, the optimal number of units in the initial fully connected layer is 128, and five residual blocks are set up, aiming to increase the model complexity and alleviate the gradient vanishing problem through the residual learning mechanism. The number of units in each residual block is 192, which moderately guarantees the representation capability. The learning rate is chosen to be 0.00245, which shows satisfactory convergence speed and stability. Each value of the above hyperparameter optimization was inputted into the corresponding model and the trained model's prediction performance was assessed; Figure 7 shows the predicted values of each specimen obtained by each model in contrast to the test values, where the blue part of the figure shows the training set data and the orange part of the test set data. Based on the prediction performance metrics in Figure 7 and Table 7, DNN has an RMSE of 85.4 on the training set and 263 on the test set, showing its lower prediction error on the training set. In contrast, ResNet has an RMSE of 111.7 on the training set and 335.7 on the test set, and although both have higher errors on the test set, DNN still has a lower test error, indicating that it is more capable of generalization. DNN has an MSE of 7287.6 on the training set and 69,173.2 on the test set, while ResNet has an MSE of 12,466.9 on the training set and 112,717.9 on the test set, which further proves that DNN fits better than ResNet on the training set, and performs relatively well on the test set, showing a better generalization ability. The MAE of DNN is 50.7 and 112.7 on the training set and test set, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Models** & **Hyperparameters** & **Search Space** & **Optimal Value** \\ \hline DNN & num\_layers & generate random integers [1; 4] & 4 \\  & units\_0 & start = 32, stop = 256, STEP = 32 & 256 \\  & activation\_0 & [”relu”, ‘tanh”, ‘sigmoid”] & relu \\  & optimizer & [’Adam’, ‘rmsprop”] & adam \\  & units\_1 & start = 32, stop = 256, STEP = 32 & 256 \\  & activation\_1 & [’relu’, ‘tanh’, ‘sigmoid”] & sigmoid \\  & units\_2 & start = 32, stop = 256, STEP = 32 & 96 \\  & activation\_2 & [’relu’, ‘tanh’, ‘sigmoid”] & relu \\ \hline ResNet & initial\_units & start = 32, stop = 256, STEP = 32 & 128 \\  & num\_blocks & [2; 5] & 5 \\  & units & start = 32, stop = 256, STEP = 32 & 192 \\  & learning\_rate & [\(1\times 10^{-1}\), \(1\times 10^{-2}\)] & 0.00245 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Hyperparameter optimization for deep machine learning models. respectively, compared to ResNet's MAE of 59.7 and 107.7, indicating that DNN is more advantageous in terms of stability and accuracy. In addition, the R\({}^{2}\) of DNN is 0.99 for the training set and 0.95 for the test set, showing a very high degree of fit, whereas the R\({}^{2}\) values of ResNet are 0.98 and 0.91, which is not a bad performance, but a slightly better fit for DNN.