Replication Data for: Inverse Bathymetry Reconstruction in Gravel-Bed Channels: A Physics-Informed Hybrid FNO-UNet Approach

This study applies a hybrid deep learning framework combining Fourier Neural Operators (FNOs), U-Net architectures, and Physics-Informed Neural Network (PINN) loss formulations for 2D bed bathymetry reconstruction and bulk flow discharge inference in gravel-bed rivers from surface velocity fields. We address the ill-posed inverse problem of inferring complex bed morphology ($B$) and unmeasured water depth ($H$) by integrating 2D Shallow Water Equations (Saint-Venant momentum and continuity constraints) with a morphological Edge-Weighted Sobel refinement module (`RefineUNet`). Pre-trained on 999 TELEMAC-2D synthetic simulations ($R^2 = 0.986$, $\text{RMSE} = 2.78\text{ mm}$), the model internalizes mass and momentum conservation principles natively in its spectral Fourier layers ($128 \times 16$ modes). Through spatial transfer learning and 10-Fold Cross-Validation across 47 audited experimental flume trials over mobile gravel substrate ($D_{50} = 40\text{ mm}$, Manning $n = 0.06\text{ s/m}^{1/3}$), the framework demonstrated monotonic performance improvements. Incorporating hydrodynamics and edge matching consistently outperformed purely data-driven baselines, advancing bathymetric reconstruction accuracy from $R^2 = 0.8840$ ($\text{RMSE} = 13.31\text{ mm}$) in the baseline to $R^2 = 0.9364$ ($\text{RMSE} = 7.51\text{ mm}$, $\text{MAE} = 4.20\text{ mm}$, dimensionless error $\text{MAE}/D_{50} = 0.105$) in the Proposed Model, with $83\%$ of trials achieving $R^2 > 0.90$. Furthermore, a dedicated weakly-supervised water depth model (`RefineUNetH`) conditioned on surface velocity ($\alpha = 0.85$) and bulk discharge ($Q_{exp}$) was coupled with a 1D-2D Bernoulli Energy Layer. The inferred 2D depth profiles preserved a strictly subcritical regime ($Fr \approx 0.10 < 1$) with zero bed-surface collisions ($H_{min} = 5.32\text{ cm} > 0$), successfully predicting bulk flow discharge with $R^2 = 0.7113$, $\text{RMSE} = 0.758\text{ L/s}$, and $\text{MAPE} = 12.03\%$. Overall, the hybrid physics-informed FNO-UNet architecture proves to be a robust surrogate for non-intrusive river bathymetry mapping and discharge estimation in data-scarce gravel-bed streams.