A Neural Operator-Based Emulator for Regional Shallow Water Dynamics
This work addresses the need for efficient forecasting in coastal areas vulnerable to climate change, representing an incremental advance in applying neural operators to domain-specific PDE problems.
The study tackled the problem of real-time forecasting of hydrodynamic processes in coastal regions by developing MITONet, a neural emulator that approximates high-dimensional numerical solvers for shallow-water equations, achieving accurate predictions in time and parametric space.
Coastal regions are particularly vulnerable to the impacts of rising sea levels and extreme weather events. Accurate real-time forecasting of hydrodynamic processes in these areas is essential for infrastructure planning and climate adaptation. In this study, we present the Multiple-Input Temporal Operator Network (MITONet), a novel autoregressive neural emulator that employs dimensionality reduction to efficiently approximate high-dimensional numerical solvers for complex, nonlinear problems that are governed by time-dependent, parameterized partial differential equations. Although MITONet is applicable to a wide range of problems, we showcase its capabilities by forecasting regional tide-driven dynamics described by the two-dimensional shallow-water equations, while incorporating initial conditions, boundary conditions, and a varying domain parameter. We demonstrate MITONet's performance in a real-world application, highlighting its ability to make accurate predictions by extrapolating both in time and parametric space.