让海岸水动力模拟可微分，实现反演与优化的一体化求解
A solver-in-the-loop framework for end-to-end differentiable coastal hydrodynamics
- 将物理演化过程构建成可微计算图，实现端到端求解
- 在4类任务中验证了对地形反演、结构优化等难题的有效性
- 适合做水动力建模与智能优化的科研人员使用
波浪传播与爬升的数值模拟是海岸工程与海啸风险评估的核心。然而，由于离散伴随方法刚性强、计算成本高，将其用于反问题（如水深估计、源项反演、结构优化）仍极为困难。本文提出AegirJAX，一种基于深度积分非静压浅水方程的全可微分水动力求解器。通过将时间推进的物理循环嵌入反向自动微分框架，该求解器将整个过程视为连续计算图。我们在一系列科学机器学习任务中验证其通用性：(1) 发现针对高度色散波传播模型误差的分域神经修正；(2) 实现断面结构的连续拓扑优化；(3) 在环路中训练递归神经网络实现主动波抵消；(4) 直接从下游传感器数据反演隐藏水深与海底滑坡运动学。所提出的可微范式从根本上模糊了正演模拟与逆向优化的界限，提供了一个统一的端到端海岸水动力框架。
原文摘要 · Abstract (English)
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.
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