Bathymetry Estimations Using Self Adaptive-Physics Informed Neural Networks on Two Dimensional Shallow Water Equations

For applications in geophysical research, coastal hazard forecasting, and marine navigation, accurate bathymetry estimation is essential. Even though they work well, conventional methods like satellite remote sensing and shipborne sonar are still costly and restricted in areas with few measurements. In this work, we assess an inverse problem of bathymetry reconstruction from two-dimensional shallow water equations using a Self-Adaptive Physics-Informed Neural Network (SA-PINN) framework. Through dynamically weighted loss terms, the model combines physical constraints with data fidelity. Five-run ablation studies show that reconstruction accuracy depends on both the network architecture and the selected loss-weight configuration. The trainable weighting mechanism provides empirical loss rescaling, while the fixed-weight experiments demonstrate sensitivity to the prescribed penalty ratio. Furthermore, we evaluate the architectural impact of Fourier feature embeddings against standard network topologies for resolving spectral topographic frequencies. To assess the framework’s reliance on ground-truth data, we conduct a sparsity ablation down to 0.1% spatial anchors and an anchor-free configuration. Reconstruction error increases substantially as bathymetry supervision is reduced, indicating continued dependence on direct bathymetric information. Finally, controlled finite-difference perturbations are used to examine the local numerical sensitivity of the trained reconstruction procedure. The resulting terms describe the response at the selected perturbation magnitude and adaptation protocol.