## 2 Materials and Methods
### Proposed Model Architecture  
Encoder-decoder architectures are powerful methods of semantic segmentation. In this type of architecture, a fully convolutional CNN serves as the encoder module, responsible for extracting feature maps that capture high-level semantic information. A decoder module is employed to gradually up-sample the CNN's output, thereby recovering the spatial information. The proposed model takes inspiration from this concept and incorporates two encoder and two decoder modules. The outputs from each are fused through a weighted average, utilizing two trainable weight parameters, W1 and W2, which are learned from the input data and optimized through the training process, where W1 is multiplied by the output of the powerful model and W2 is multiplied by the output of the lightweight model, and the resulting values are combined through element-wise addition. This combined output is subsequently processed through a fully connected layer and a sigmoid-activation function, leading to the final pixel-wise classification. This novel approach increases the input for the final classification task, thus enhancing performance, particularly given the constraints of a relatively small dataset. Furthermore, both encoder modules in our architecture are CNNs that have been pre-trained on ImageNet, then subsequently fine-tuned with the Sen1 Floods11 dataset. A visual representation of this architecture is presented in Figure 3.  
Figure 3: Diagram of the proposed model architecture in which dual encoder-decoder models are adopted. The weights (W1 and W2) are trained parameters that are multiplied by the output of  
each model before being combined to obtain the final prediction. Gradient-weighted class activation mapping is then applied: the water class score is obtained, and the gradients are set to one before being backpropagated through global average pooling. A weighted combination of the resulting activation maps is computed and passed through ReLU to provide a heatmap showing the pixels with a positive impact on the prediction. The architecture leverages two distinct CNN models as encoder modules. One of these models is a high-performance CNN with robust computational accuracy, whereas the other is a more lightweight CNN, designed for greater computational efficiency. This strategic combination ensures that the two encoder modules complement each other, resulting in an overall model with higher accuracy while maintaining efficient training and prediction times. The more robust encoder module employs repetitive convolutional and identity blocks [36], each consisting of 3 convolutional layers: a 1 \(\times\) 1 convolution, a 3 \(\times\) 3 convolution, and an additional 1 \(\times\) 1 convolution. An identity block, functioning as a skip-connection, feeds the activation function from the final convolutional layer into a deeper network layer, effectively mitigating the vanishing-gradient problem often encountered in deep neural networks. The lighter encoder module comprises 17 recurring blocks, each encompassing 3 layers: a 1 \(\times\) 1 convolution featuring Rectified Linear Unit (ReLU) activation, a depthwise convolution, and an additional 1 \(\times\) 1 convolution. The decoder modules within the proposed architecture perform up-sampling, where transposed convolution is applied to the feature maps originating from the encoder CNNs, producing a high-resolution output that recovers the spatial information lost by the encoder module. To achieve this effectively, each decoder module employs a range of performance-enhancing features. The first decoder includes dense skip pathways and deep supervision, whereas the second involves atrous convolution, spatial pyramid pooling, and depthwise separable convolution. Dense skip pathways serve to minimize the semantic gap between the encoder and decoder modules, facilitating a dense convolution on the feature maps from the encoder module. This reduces the complexity of the optimizer's task, resulting in more efficient optimization.