## 3 Application of Model-Agnostic Meta-Learning (MAML) Model
### MAML Model
```
Input: Point set \(\mathbf{X}\) with 19 characteristics and 436 samples  Label set \(\mathbf{Y}\) with 1 characteristic and 436 samples Training parameter: \(\theta\)-weights and bias in the net Hyper parameter: epoch1-The number of times each task was trained in the MAML epoch2-The number of times each task was trained in the Fine-tune \(\alpha\)-parameters to control the learning rate of the net \(\beta\)-parameters to control the learning rate of the task Data segmentation: 1. Divide the samples into training set and test set2. Divide the training set into M tasks, the test set into N tasks Steps in the MAML: 1. \(\theta\) initialization for\(\mathbf{\mathrm{f}}\) = 1,..., epoch1  for batches of tasks in M tasks \(\mathbf{\mathrm{f}}\) \(\theta_{temp}\) initialization and get \(\hat{y}(X,\theta)\) by forward propagation \(\theta_{temp}\) Calculate the loss of each task \(l_{m_{t}}\ =\ \sum\limits_{i}^{m}\left(y-\hat{y}(X,\theta)\right)^{2}/m\) \(\theta_{temp}\) Update \(\theta_{temp}\) for \(\mathbf{\mathrm{f}}\) times \(\theta_{m_{t}}^{i}\ =\ \theta_{m_{t}}^{i-1}-\alpha\
abla_{\theta_{m_{t}}^{i-1}l_{m_{t}}} \left(\theta_{m_{t}}^{i-1}\right)\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\) \(\theta_{m_{t}}^{i}\)
```  
**Algorithm 1** Algorithm of MAML. The steps outlined in Algorithm 1 describe the MAML process comprehensively. The notation '\(\hat{y}\)' is the current training time,'m' represents the sample number, \(\hat{y}(X,\theta)\) is the predicted value, \(\theta^{\prime}\) represents the updated weights and biases at the current training time, '\(\hat{y}\)' is the labeled value, \(\theta_{temp}\) is a temporary parameter used to search for gradient descent directions, \(m_{B}\) is the number of tasks in a batch, \(m_{t}\) is the \(m_{t}\)-_th_ task in the train, \(\hat{\theta}\) is the notation of a partial differential, \(w\) is the component of array \(\theta\) which represents a single weight or bias value, 'L' is the loss function of the regression problem, and \(\
abla\) is the gradient of the variable. The MAML model has three assumptions. The first is the fast adaptation assumption. Under this assumption, the MAML model can achieve good performance on a new task with just a few gradient updates, meaning that the initial parameters obtained through meta-training are close to the optimal parameters in the task space. The second is the shared parameter assumption. Under this assumption, although tasks are different, they can share the same model's initialization parameters, namely its meta-parameters. These meta-parameters are learned through an optimization process across multiple tasks. The third is the finite sample assumption. Under this assumption, for each task only a small number of training samples (usually referred to as K-shot learning) are needed to adapt the model. This assumption is aligned with the goal of MAML, which is to achieve rapid learning. This research utilizes two databases, Meta1 and Meta2, to develop the MAML model. The Meta1 database considers the CFRP-to-concrete interfacial ultimate loads under different environments (hygrothermal or salt attack) separately. The coupled database possesses features that influence the interfacial ultimate load under both wet-dry attacks and salt attacks, enabling the MAML model to perform transfer learning between these two domains during training. This enhances the model's generalization ability and performance on new tasks, making it applicable to data obtained from both wet-dry attack and salt attack environments. The Meta2 database is entirely unrelated to the Meta1 database; it considers the interfacial ultimate load under the joint action of sulfate ions and wet-dry cycle environments.