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.

翻译：沿海区域与河流洪泛区极易受到极端天气事件的影响。对这些区域的水动力过程进行精确的实时预报，对于基础设施规划和气候适应至关重要。然而，高保真数值模型的计算成本通常过高，难以用于实时预报；而传统模型降阶算法或常规神经网络等低成本方法，通常难以泛化到分布外条件。在本研究中，我们提出了多输入时序算子网络（MITONet），这是一种新颖的自回归神经仿真器，它利用隐空间算子学习，高效地逼近用于求解由时变、参数化偏微分方程控制的复杂非线性问题的高维数值求解器。我们通过预测纽约州辛内科克湾口的区域潮汐驱动动力学以及路易斯安那州红河某河段的河流流动，展示了MITONet的预测能力。这两个案例均用二维浅水方程（2D SWE）描述，并同时考虑了初始条件、时变边界条件以及底部摩擦系数等域参数。尽管所研究的流动状态、复杂几何结构与网格以及底部摩擦系数范围差异显著，MITONet始终表现出卓越的预测能力：异常相关系数高于0.9，最大归一化均方根误差为0.011，计算加速比达到100倍至1250倍。即使是在随机初始条件和未见过的参数值下进行长达175天的自回归滚动预测，其性能依然稳健。