## 2 Materials and Methods
### Steps of Weather Disaster Emergency Response Capability Feature Extraction
#### 2.4.2 RNN Autoencoder Training  
The RNN autoencoder used for feature extraction is solved by the BPTT algorithm and combined with a gradient-based parameter optimization method for model training. The gradient of the loss \(L\) to the current node is first calculated recursively based on the output gradient of the last moment of decoder part d in Figure 2, and then the model parameters are updated according to the gradient direction.  
Starting from the loss at the final moment recursively, the total loss \(L\) is obtained as shown in Equation (23) for moment \(t\) and loss \(L^{(t)}\) of the gradient.  
\[\frac{\partial L}{\partial L^{(t)}}=1 \tag{26}\]  
On this basis, the reconstruction error of the capability input feature \(x\) is passed backwards in the direction of the output of the delay decoder to the \(t\)th output moment, and the total loss \(L\) is obtained for the moment \(t\) and output \(\hat{x}\) of the gradient.  
\[\frac{\partial L}{\partial\hat{x}_{i}^{(t)}}=\frac{\partial L}{\partial L^{(t) }}\;\frac{\partial L^{(t)}}{\partial\hat{x}_{i}^{(t)}}=\frac{\partial L^{(t)}} {\partial\hat{x}_{i}^{(t)}} \tag{27}\]The specific computation process starts at the end of the sequence (moment \(T\)) and is performed in reverse. At the moment \(T\), the \({h^{\prime}}^{(T)}\), and there is no subsequent node, so its gradient is  
\[\frac{\partial L}{\partial{h^{\prime}}^{(T)}}=\frac{\partial L}{\partial\dot{x} ^{(T)}}\ \frac{\partial\dot{x}^{(T)}}{\partial{h^{\prime}}^{(T)}}=W_{{h^{\prime}}x}{}^{ T}\ \frac{\partial L}{\partial\dot{x}^{(T)}} \tag{28}\]  
The gradient is then propagated backwards through time due to the fact that, when \(t<T\) time, the \({h^{\prime}}^{(T)}\) has \({h^{\prime}}^{(t+1)}\) and \(\dot{x}^{(T)}\) as two subsequent nodes, and its gradient is calculated as  
\[\frac{\partial L}{\partial{h^{\prime}}^{(t)}}=\frac{\partial L}{\partial\dot {x}^{(t)}}\ \frac{\partial\dot{x}^{(t)}}{\partial{h^{\prime}}^{(t)}}+\frac{\partial L}{ \partial{h^{\prime}}^{(t+1)}}\ \frac{\partial{h^{\prime}}^{(t+1)}}{\partial{h^{\prime}}^{(t)}}=W_{{h^{ \prime}}x}{}^{T}\ \frac{\partial L}{\partial\dot{x}^{(t)}}+W_{{h^{\prime}}{h^{\prime}}}{}^{T} \ \frac{\partial L}{\partial{h^{\prime}}^{(t+1)}} \tag{29}\]  
The gradient of the internal nodes is calculated, and the gradient of the loss about the parameters can be found. Because RNN autoencoders share parameters at multiple moments, to remove ambiguity, it is defined to use a dummy variable at moment \(t\)\(W^{(t)}\) as \(W\) for a copy of the loss, and then the gradient of the loss about the weights is found, respectively.  
\[\frac{\partial L}{\partial W_{{h^{\prime}}x}}=\sum_{t}\sum_{i}\frac{\partial L }{\partial\dot{x}_{i}^{(t)}}\ \frac{\partial\dot{x}_{i}^{(t)}}{\partial{W_{{h^{\prime}}x}}^{(t)}}=\sum_{t} \frac{\partial L}{\partial\dot{x}^{(t)}}\ {h^{\prime}}^{T} \tag{30}\]  
\[\frac{\partial L}{\partial W_{{h^{\prime}}{h^{\prime}}}}=\sum_{t}\sum_{i} \frac{\partial L}{\partial{h^{\prime}_{i}}^{(t)}}\ \frac{\partial{h^{\prime}_{i}}^{(t)}}{\partial{W_{{h^{\prime}}{h^{\prime}}}}^ {(t)}}=\sum_{t}W_{{h^{\prime}}x}{}^{T}\ \frac{\partial L}{\partial\dot{x}^{(t)}}+W_{{h^{\prime}}{h^{\prime}}}{}^{T} \ \frac{\partial L}{\partial{h^{\prime}}^{(t+1)}}\ {h^{\prime}}^{(t-1)}{}^{T} \tag{31}\]  
According to the calculated gradients \(\frac{\partial L}{\partial W_{{h^{\prime}}x}}\) and \(\frac{\partial L}{\partial W_{{h^{\prime}}{The algorithm trains an RNN autoencoder to extract capability features from the input sequence samples \(S\). The algorithm uses a forward computation to obtain the final hidden state vector \(a\), which is the coding result of the sample. The algorithm then reconstructs the input sequence from the coding result and calculates the loss function for the sample reconstruction. The weights and biases of the capability feature extraction model are updated using the gradient descent algorithm, until the maximum number of iterations \(K\) is reached, or the error falls below the specified upper limit \(E\).