## 3 Experiments
### Loss Function and Training Strategy  
For seafloor terrain reconstruction, the design of the loss function is critical, ensuring a balance between numerical accuracy and structural integrity preservation. We propose a multi-objective joint loss function comprising the RMSE, Structural Similarity Index Measure (SSIM), and an uncertainty quantification regularization term. The RMSE directly measures the deviation between predicted and actual values, ensuring the precise reconstruction of metrics like depth or elevation, which can be expressed as  
\[RMSE=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left(y_{i}-\hat{y_{i}}\right)^{2}} \tag{14}\]  
Here, \(N\) represents the number of samples, is the true value for the i-th sample, and is the corresponding prediction.  
SSIM captures local structural features such as trenches, ridges, and slopes, enhancing visual and structural quality. Then, the expression of the loss function is  
\[L_{SSIM}=1-\frac{(2\mu_{y}\mu_{y}+C_{1})\cdot(2\sigma_{yy}+C_{2})}{(\mu_{y}^{2 }+\mu_{y}^{2}+C_{1})\cdot(\sigma_{y}^{2}+\sigma_{y}^{2}+C_{2})} \tag{15}\]  
Here, \(\mu_{y}^{2}\) and \(\mu_{y}^{2}\) represent the mean of the original and reconstructed images, \(\sigma_{y}^{2}\) and \(\sigma_{y}^{2}\) denote their variance, \(\sigma_{yy}\) indicates the covariance between the original and reconstructed images, and \(C_{1}\) and \(C_{2}\) are constants introduced to avoid division by zero.  
\(L_{total}\) is calculated as follows: parameters \(\alpha\) and \(\beta\) modulate these components, preventing RMSE from overlooking local details and compensating for SSIM's pixel-level precision limitations.  
\[L_{total}=\alpha\;*\;RMSE+\beta\;*\;L_{SSIM} \tag{16}\]  
Additionally, the uncertainty quantification regularization term offers probabilistic insights and enhances regularization, improving model robustness in complex scenarios. Training optimizations include Adam optimizer with GradScaler and autocast for  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & **Grid Spacing** & **Additional Information** & **Data Access** \\ \hline
1 & 1 arcsecond & Bass Strait Bathymetry, 2022, 30 m & [[http://pid.geoscience.gov.au/dataset/ga/147043](http://pid.geoscience.gov.au/dataset/ga/147043)]([http://pid.geoscience.gov.au/dataset/ga/147043](http://pid.geoscience.gov.au/dataset/ga/147043)) (accessed on 23 November 2024) \\
2 & 1 arcsecond & Australian Bathymetry Topography & [[https://pid.geoscience.gov.au/dataset/ga/144348](https://pid.geoscience.gov.au/dataset/ga/144348)]([https://pid.geoscience.gov.au/dataset/ga/144348](https://pid.geoscience.gov.au/dataset/ga/144348)) (accessed on 23 November 2024) \\  & & Great Barrier Reef A, 2020, 30 m, 10–17° S, & 143–147° E & \\  & & Great Barrier Reef B, 2020, 30 m, 16–23° S, & \\
3 & 1 arcsecond & Great Barrier Reef C, 2020, 30 m, 18–24° S, & \\  & & Great Barrier Reef D, 2020, 30 m, 23–29° S, & \\  & & 150–156° E & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Information about HR regional DBM datasets.  
mixed precision and dynamic learning rate adjustment via ReduceLROnPlateau (starting at 1 \(\times\) 10\({}^{-4}\)) over a maximum of 200 epochs. This approach effectively balances numerical accuracy and structural fidelity, meeting rigorous demands for seafloor terrain reconstruction.