## 3 Application of Model-Agnostic Meta-Learning (MAML) Model
### Comparison between MAML and Previous Analytical Models  
In recent years, with the increasing application of deep learning in various engineering fields, there has been a growing number of cases where scholars in the field of civil engineering tend to use traditional ANN models, namely, backward propagation algorithms, for implicit regression problems. As shown in Figure 2, traditional neural networks are mainly divided into two groups: forward propagation and backward propagation. During forward propagation, with m training samples available, where \(\mathbf{X}\) represents input variables and \(\mathbf{y}\) represents output results, these m samples can be represented as \(\left\{\left(x^{(1)},y^{(1)}\right),\left(x^{(2)},y^{(2)}\right),...,\left(x^ {(m)},y^{(m)}\right)\right\}\). Input variable \(\mathbf{X}\) is represented as an \(\mathbf{\mathrm{m}}\times\mathbf{\mathrm{n}}_{\mathrm{x}}\) matrix, where \(\mathbf{\mathrm{m}}\) denotes the number of training samples and \(\mathbf{\mathrm{n}}_{\mathrm{x}}\) represents the dimensionality of the input feature vectors. Similarly, output variable \(\mathbf{y}\) is represented as an \(\mathbf{\mathrm{m}}\times\mathbf{\mathrm{n}}_{\mathrm{y}}\) matrix, with \(\mathbf{\mathrm{m}}\) denoting the number of training samples and \(\mathbf{\mathrm{n}}_{\mathrm{y}}\) representing the dimensionality of the output feature vectors. The above is the preparation of the dataset before training. It is clearly indicated in Figure 3 that the input matrix \(\mathbf{X}\) undergoes computations through the hidden layers of the neural network, where each layer calculates its respective formulaic results and applies an activation function (typically ReLU) to generate the  
Figure 2: Structure diagram of traditional neural network algorithm. layer's output results. Eventually, these computations culminate in the final output \(\hat{y}\); this is the process of forward propagation. Back propagation differs; forward propagation calculated the predicted value \(\hat{y}\) and then used the loss function to calculate the difference (**L**) between the predicted value \(\hat{y}\) and the actual value \(y\). In the process of backpropagation, the gradients of each layer's parameters \(\
abla_{\theta}\), calculated based on the loss function, are computed in reverse order, starting from the last layer. Subsequently, the weights of each layer are adjusted layer by layer (\(\theta~{}=~{}\theta-\alpha\
abla_{\theta}L\)), ultimately updating the parameters. This iterative procedure leads to a gradual decrease in the loss function **L** and thereby constitutes the backpropagation process. In this section, a comparison is made between the BPNN, a widely used algorithm in civil engineering for implicit regression problems, and the MAML algorithm in their predictions of the degradation level of CFRP-to-concrete interface bond strength under the coupling effect of hydrothermal and salt attacks. This aims to demonstrate that the MAML algorithm, suitable for few-shot learning, is more appropriate for addressing complex implicit regression problems. To ensure a more reliable comparison of the predictive results between BPNN and MAML, the same database is adopted. The following content compares the accuracy of the predictive results, the fitting capability of the network models, and the convergence speed and precision of the two algorithms. Figure 3 illustrates the comparison between the prediction results of both the MAML and BPNN using the database Meta2. A total of two repeated tests are conducted to avoid randomness. The x-axis represents the sample number of the test set, while the y-axis denotes the normalized bond strength. The black line represents the true values of 20 test samples, the red line represents the predicted values of the MAML algorithm, and the blue line represents the predicted values of the BPNN algorithm. As shown in Figure 3, it can be observed that the predicted results of the BPNN in both tests are significantly higher than the true values.