## 3 Application of Model-Agnostic Meta-Learning (MAML) Model
### MAML Model  
Unlike conventional neural networks, which optimize learning outcomes based on individual samples, the MAML algorithm focuses on tasks as its training target, thereby creating the learning process. Instead of directly acquiring a mathematical model for prediction, it aims to learn \"how to learn a mathematical model more efficiently and effectively.\" MAML is primarily divided into two components: meta-learning and fine-tuning processes. Meta-learning involves designing model characteristics that can be shared across various tasks, facilitating these characteristics' adjustments. Its objective \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Serial Number** & **Parameter Range** & **1** & **2** & **80** \\ \hline Ultimate Load (KN) & 5.80–22.90 & 16.60 & 18.10 & \(\dots\) & 6.40 \\ \hline \hline \end{tabular} This table is for illustration purposes only, with more data presented in Table S2.  
\end{table} 
Table 4: Data Y in the Meta2 database. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Serial Number and** & **Parameter Range** & **1** & **2** & **80** \\ \hline
1—Chloride Concentration (\%) & 0–0 & 0 & 0 & \(\dots\) & 0 \\
2—Salfate Concentration (\%) & 0–10.00 & 10.00 & 10.00 & \(\dots\) & 5.00 \\
3—Cycles (d) & 0–150.00 & 30.00 & 30.00 & \(\dots\) & 90.00 \\
4—Soaking Time (h) & 6.00–12.00 & 12.00 & 12.00 & \(\dots\) & 6.00 \\
5—Drying Time (h) & 1.00–4.00 & 4.00 & 4.00 & \(\dots\) & 1.00 \\
6—Heating Time (h) & 5.00–8.00 & 8.00 & 8.00 & \(\dots\) & 5.00 \\
7—Temperature (\({}^{\circ}\)C) & 0–0 & 0 & 0 & \(\dots\) & 0 \\
8—Humidity (\%) & 100.00–100.00 & 100.00 & 100.00 & \(\dots\) & 100.00 \\
9—Soaking Temperature (\({}^{\circ}\)C) & 25.00–30.00 & 25.00 & 25.00 & \(\dots\) & 30.00 \\
10—Drying Temperature (\({}^{\circ}\)C) & 25.00–25.00 & 25.00 & 25.00 & \(\dots\) & 25.00 \\
11—Heating Temperature (\({}^{\circ}\)C) & 40.00–40.00 & 40.00 & 40.00 & \(\dots\) & 40.00 \\
12—Paste Length (mm) & 60.00–180.00 & 60.00 & 80.00 & \(\dots\) & 100.00 \\
13—Paste Layers & 1.00–1.00 & 1.00 & 1.00 & \(\dots\) & 1.00 \\
14—CFRP Tensile Strength (Mpa) & 3106.000–3659.000 & 3659.00 & 3659.00 & \(\dots\) & 3106.00 \\
15—CFRP Elastic Modulus (Gpa) & 256.000–275.6000 & 265.00 & 265.00 & \(\dots\) & 275.60 \\
16—CFRP Elongation (\%) & 1.5860–1.7140 & 1.714 & 1.714 & \(\dots\) & 1.586 \\
17—CFRP Surface Density (g/m\({}^{2}\)) & 205.000–300.6000 & 205.00 & 205.00 & \(\dots\) & 300.60 \\
18—CFRP Dimensions (mm\({}^{3}\)) & 115.2000–835.0000 & 115.20 & 153.60 & \(\dots\) & 835.00 \\
19—Concrete Strength (Mpa) & 18.3500–54.4000 & 34.16 & 34.16 & \(\dots\) & 31.60 \\ \hline \hline \end{tabular} This table is for illustration purposes only, with more data presented in Table S2.  
\end{table} 
Table 3: Data X in the Meta2 database. is to train the model on a series of related tasks to gather useful general knowledge for tackling new tasks. The meta-learning training process entails iterative tasks, wherein the model utilizes its current parameters for each task and computes the loss specific to that task. Subsequently, the model parameters are updated by calculating a weighted average of the losses across these tasks. Fine-tuning takes place after meta-learning (as delineated in the fine-tune steps in Algorithm 1), during which the model's parameters are fixed and further adjustments are made to adapt to specific new tasks. This fine-tuning stage resembles traditional machine learning training. Throughout fine-tuning, the model is trained using data from new tasks, adjusting parameters via gradient descent to minimize the loss function associated with the new tasks. Since the model's initial parameters have been optimized during meta-learning, the fine-tuning training process typically requires fewer iterations and can swiftly adapt to new tasks. Consequently, even with limited existing data, MAML can still achieve high accuracy.