## 2 Materials and Methods
### The Prediction Model of ECRNet
#### 2.3.2 Modified Neural Network  
The modified neural network aims to establish a short-term dynamic model to compensate and adjust the prediction bias accumulation in the long-term mode of the prediction model. Inspired by the emotion modulation mechanism, the prediction bias of the LSTM model in different ocean layers is modified by two correction strategies. 1. Proactive Modulation Module  
The structure of the Proactive Modulation module is shown in Figure 6. The input of it consists of two parts which includes the prediction result \(y\prime_{t}\) of the base prediction model and the \(x_{t}\) obtained by matrix selection of the features in the feature factor data set \(X_{t}\). The Proactive Modulation module is mainly composed of two evaluation functions and output functions, and its specific workflow is as follows. The first step of it is that the \(z\) variable in the input \(y\prime_{t}\) is judged by the \(\mu(z)\) function to decide whether to enter the module for correction. The formula of \(\mu(z)\) is as Equation (6):  
\[\mu(z)= \begin{cases}1\,,&z<-200\\ 0\,,&z\geq-200\end{cases} , \tag{6}\]  
where \(z\) represents the depth of the AUV drift predicted by the base model. It can be seen from Equation (6) that the value of \(\mu(z)\) is 1 when \(z<-200\), and then the Proactive Modulation module is activated. The input \(x_{t}\) is processed through the full connection layer with tanh as the activation function to obtain the position state information \(h_{t}\) at the current time. The formula is as Equation (7):  
\[h_{t}=\tan\mathrm{h}(W_{h}\cdot x_{t}+b_{h}) \tag{7}\]  
The next step is to process and evaluate the two parts of location information \(h_{t}\) and \(y\prime_{t}\) through two evaluation functions. This step is divided into two parts. The first part operation is handled by an evaluation emphasis function \(e_{t}\) to obtain emphasis information \(E_{t}\). Based on the function, by examining and comparing the information between \(x_{t}\) and \(x_{t-1}\) to output a value of 0-1. The closer the value is to 1, the higher the degree of emphasis is. The closer the value is to 0, the information will be ignored. The formula is as Equation (8):  
\[e_{t}=\sigma(W_{e}\cdot[x_{t},x_{t-1}]+b_{e}), \tag{8}\] \[E_{t}=e_{t}\ast h_{t}\]  
The next operation is handled by an evaluation neglect function \(g_{t}\) to decide what information to ignore to obtain the final information \(N_{t}\). The formula is as Equation (9):  
\[g_{t}=\sigma(W_{g}\cdot[x_{t},x_{t-1}]+b_{g}), \tag{9}\] \[N_{t}=g_{t}\ast y\prime_{t}\]  
Figure 6: Structure of Proactive Modulation Module. The last step is that the modified prediction result \(y_{t}\) is obtained through the selectivity of the output function to the information modified by the rating function. The formula is as Equation (10):  
\[ \begin{array}{c}y_{t}=\varphi_{t}\cdot\tan\text{h}(O_{t})\\ \varphi_{t}=\begin{array}{c}\tan\text{h}\big{(}W_{\varphi}\cdot[x_{t},x_{t-1} \big{)}\big{)}\\ O_{t}=N_{t}+E_{t}\end{array}\end{array}  \tag{10}\]  
To help the model learn more accurately and quickly, the value score of each feature is calculated and normalized based on the principle of permutation feature importance [28]. The value score of each feature is used as the initialization parameter of the AUV drift track prediction model to help the model converge quickly and save the training prediction time to get the global optimal solution. Firstly, based on the trained base prediction model, random shuffle is performed for one feature column at a time. Then, input the model for prediction, and record each feature column of change and its corresponding Loss. Each Loss is the corresponding feature importance. The greater the Loss, the more important the feature is to the model.