A solver-in-the-loop framework for end-to-end differentiable coastal hydrodynamics

TL;DR

This paper introduces AegirJAX, a fully differentiable hydrodynamic solver enabling efficient inverse problems and optimization in coastal engineering using automatic differentiation.

Contribution

It presents AegirJAX, a novel differentiable solver based on shallow-water equations, facilitating inverse modeling and optimization tasks in coastal hydrodynamics.

Findings

Demonstrated neural corrections for wave model misspecifications.

Achieved topology optimization for breakwater design.

Enabled bathymetry and landslide inversion from sensor data.

Abstract

Numerical simulation of wave propagation and run-up is a cornerstone of coastal engineering and tsunami hazard assessment. However, applying these forward models to inverse problems, such as bathymetry estimation, source inversion, and structural optimization, remains notoriously difficult due to the rigidity and high computational cost of deriving discrete adjoints. In this paper, we introduce AegirJAX, a fully differentiable hydrodynamic solver based on the depth-integrated, non-hydrostatic shallow-water equations. By implementing the solver entirely within a reverse-mode automatic differentiation framework, AegirJAX treats the time-marching physics loop as a continuous computational graph. We demonstrate the framework's versatility across a suite of scientific machine learning tasks: (1) discovering regime-specific neural corrections for model misspecifications in highly dispersive wave propagation; (2) performing continuous topology optimization for breakwater design; (3) training recurrent neural networks in-the-loop for active wave cancellation; and (4) inverting hidden bathymetry and submarine landslide kinematics directly from downstream sensor data. The proposed differentiable paradigm fundamentally blurs the line between forward simulation and inverse optimization, offering a unified, end-to-end framework for coastal hydrodynamics.