arXiv:2502.14782cs.CEcs.LG2025-02

用神经算子模型快速精准模拟沿海与河流水动力,实时预报更高效。

A Neural Operator Emulator for Coastal and Riverine Shallow Water Dynamics

  • 基于隐空间算子学习的自回归网络,融合多输入与动态边界条件。
  • 预测相关系数超0.9,误差低于0.011,推理速度提升100至1250倍。
  • 适用于复杂地形与未知参数,适合气候适应与防洪实时预警场景。

沿海地区和河流泛滥平原极易受极端天气影响。准确的实时水动力预报对基础设施规划和气候适应至关重要。然而,高保真数值模型计算成本过高,难以实时使用;传统降阶算法或普通神经网络又常无法泛化到分布外情况。本文提出多输入时序算子网络(MITONet),一种基于隐空间算子学习的自回归神经模拟器,可高效逼近由时变参数偏微分方程支配的复杂非线性问题的高维数值求解器。我们在纽约辛内克洛克入口区域的潮汐驱动动力学和路易斯安那州红河段的河流流动上验证了其性能,两者均由二维浅水方程(2D SWE)描述,涵盖初始条件、时变边界条件及底摩擦系数等域参数。尽管流态、几何结构与网格差异显著,且底摩擦系数范围广泛,MITONet仍保持一致高精度预测,异常相关系数高于0.9,最大归一化均方根误差为0.011,计算速度提升100倍至1250倍,即使在随机初始条件与未见参数值下进行长达175天的自回归滚动预测也表现优异。

原文摘要 · Abstract (English)

Coastal regions and river floodplains are particularly vulnerable to the impacts of extreme weather events. Accurate real-time forecasting of hydrodynamic processes in these areas is essential for infrastructure planning and climate adaptation. Yet high-fidelity numerical models are often too computationally expensive for real-time use, and lower-cost approaches, such as traditional model order reduction algorithms or conventional neural networks, typically struggle to generalize to out-of-distribution conditions. In this study, we present the Multiple-Input Temporal Operator Network (MITONet), a novel autoregressive neural emulator that employs latent-space operator learning to efficiently approximate high-dimensional numerical solvers for complex, nonlinear problems that are governed by time-dependent, parameterized partial differential equations. We showcase MITONet's predictive capabilities by forecasting regional tide-driven dynamics in the Shinnecock Inlet in New York and riverine flow in a section of the Red River in Louisiana, both described by the two-dimensional shallow-water equations (2D SWE), while incorporating initial conditions, time-varying boundary conditions, and domain parameters such as the bottom friction coefficient. Despite the distinct flow regimes, the complex geometries and meshes, and the wide range of bottom friction coefficients studied, MITONet displays consistently high predictive skill, with anomaly correlation coefficients above 0.9, a maximum normalized root mean square error of 0.011, and computational speedups between 100x-1,250x, even for 175 days of autoregressive rollout forecast from random initial conditions and with unseen parameter values.

神经算子水动力模拟实时预报浅水方程

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