A Neural Operator-Based Emulator for Regional Shallow Water Dynamics

2025-02-20

AI Summary

Coastal regions face escalating threats from sea-level rise and extreme weather, necessitating real-time, high-fidelity hydrodynamic forecasting to inform climate-resilient infrastructure planning. To address this, we propose MITONet—a multi-input temporal neural operator network that uniquely integrates dimensionality reduction with an autoregressive architecture for efficient modeling of parameterized shallow-water-equation-driven tidal dynamics. MITONet jointly encodes initial/boundary conditions and spatially varying domain parameters, enabling robust extrapolation both temporally (over several hours) and parametrically (beyond the training range by >30%). Evaluated on realistic coastal scenarios, it achieves millisecond-scale inference latency while reducing prediction error by 52% relative to conventional surrogate models. This marks a significant advance in overcoming the dual bottlenecks—real-time performance and generalizability—that have long constrained numerical solvers in operational coastal forecasting.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Time-Series/Data Streams
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

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.

Problem

• Accurate real-time coastal hydrodynamic forecasting
• Efficient approximation of high-dimensional numerical solvers
• Extrapolation in time and parametric space

Innovation

• Neural operator-based emulator
• Dimensionality reduction technique
• Autoregressive neural network model