Abstract We present two methods to estimate bottom topography in a shallow water flow using only surface deformation measurements. One is based on Physics‐Informed Neural Networks (PINNs) and the other on the Adjoint State Method. We test both methods using synthetic data in 1D and 2D cases. Both are able to successfully reconstruct not only the bottom topography but also the surface velocity. Both also show robustness against noise and data sparsity up to reasonable levels.
Pancotto et al. (2026) studied this question.