Estimating bottom topography in shallow water flows

TL;DR

This paper introduces two novel methods, PINNs and Adjoint State Method, for estimating bottom topography in shallow water flows solely from surface deformation data, demonstrating robustness and accuracy.

Contribution

The paper presents two new approaches for bottom topography estimation using surface measurements, combining physics-informed neural networks and adjoint methods.

Findings

Both methods successfully reconstruct bottom topography and surface velocity.

Methods are robust against noise and data sparsity.

Validated on synthetic 1D and 2D data.

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.