## 3 Application of Model-Agnostic Meta-Learning (MAML) Model
### Comparison between MAML and Previous Analytical Models
Moreover, after regularization, most of the predicted values of the BPNN are distributed between 0.15 and 0.20. For samples with lower strength, the BPNN does not exhibit satisfactory learning results, indicating that the network's learning ability is limited and the results are underfitting. The main reason for the underfitting is the low sample size, which is also one of the important limitations of neural network algorithms in practical engineering applications. For the MAML algorithm, which incorporates prior knowledge, as shown by the red line in Figure 3, the predictive results are significantly superior to those of the BPNN algorithm. Moreover, it achieves better fitting results for both larger and smaller values. Figure 4 provides a more intuitive comparison of the fitting capabilities of the two algorithms. Figure 3: Comparation between MAML and BPNN’s prediction results. Figure 4 depicts the fitting of the predictions of two algorithms. The black line in the middle represents perfect fitting, where the predicted values match the actual values. The red portion represents prediction data from the MAML algorithm, while the blue portion represents prediction data from the BPNN algorithm. The \(R^{2}\) value indicates the slope of the scatter fit to the line, with values closer to 1.0 indicating a closer approximation to perfection. It can be observed that the computational results of the MAML algorithm are primarily distributed near the curve of perfect fitting, with the fitting results from two repeated predictions being almost identical, with R-squared values of 0.9137 and 0.9472, respectively. On the other hand, the computational results of the BPNN mostly cluster in the top-left of the graph, indicating that the neural network struggles to predict results effectively as the actual values decrease. This discrepancy highlights the superior predictive performance of MAML, compared to BPNN, of this complex task. The loss function reflects the difference between the predicted values and the actual values. The closer the loss function is to zero, the closer the predicted values are to the actual values. This function is a crucial variable in the learning process of neural networks, and its evolution pattern represents the learning path or process of the neural network. Figure 5 illustrates the comparison of loss functions during the training and testing processes of two neural network algorithms. Figure 5 provides a comparative analysis of the training and testing losses of MAML and BPNN across different numbers of repeated tests. Barring the initial phase, MAML  
Figure 4: Comparation of the fitting degree between the predicted results of the BPNN and MAML and the actual results. Figure 5: Evolution trend of loss function of two algorithms. consistently exhibits lower training losses than BPNN. The training loss of MAML swiftly approaches zero and steadily converges after a relatively short number of epochs, whereas BPNN's training loss fluctuates with increasing epochs, displaying a tendency to remain largely unconverged and frequently showcasing outliers. It is not surprising that the BPNN algorithm fails to converge in its prediction on this database. After all, with only around 80 samples, and not all of them being high-quality, the dataset falls far short of the big data requirements of neural network algorithms. On the contrary, both in training and testing, the MAML algorithm converges rapidly on this small sample database. In summary of this section, it is evident that MAML demonstrates superior applicability and accuracy in predicting the CFRP-to-concrete interfacial bond strength affected by the coupling effect of hydrothermal and salt ion attacks. However, this does not imply that the MAML algorithm universally outperforms the BPNN algorithm. When the database is sufficiently abundant and of high quality, the superiority of the BPNN algorithm has been demonstrated.