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

2026-04-08

AI Summary

Traditional coastal hydrodynamic models struggle to efficiently solve inverse problems due to the complexity of adjoint derivative derivation and high computational costs. This work proposes AegirJAX, an end-to-end differentiable solver that, for the first time, formulates the entire process based on depth-integrated non-hydrostatic shallow water equations as a continuous computational graph embedded within the JAX automatic differentiation framework, thereby unifying forward simulation and backward optimization. The method enables a range of scientific machine learning tasks—including neural network correction, topology optimization, and parameter inversion—and has been successfully applied to dispersive wave modeling, breakwater optimization, active wave cancellation, and inversion of seabed topography and landslide kinematics, significantly enhancing both the efficiency and accuracy of inverse problem solutions.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Hardware-aware ML
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

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.

Problem

• coastal hydrodynamics
• inverse problems
• bathymetry estimation
• source inversion
• structural optimization

Innovation

• differentiable simulation
• coastal hydrodynamics
• automatic differentiation
• inverse problems
• scientific machine learning