Principled Operator Learning in Ocean Dynamics: The Role of Temporal Structure

2025-10-10

AI Summary

To address poor physical consistency, inadequate high-frequency process modeling, and weak stability in high-resolution, long-term ocean dynamics forecasting, this paper proposes FNOtD: a Fourier neural operator (FNO) variant that explicitly incorporates dispersion relation constraints and jointly learns spatiotemporal integration kernels, enabling multi-scale wave propagation modeling guided by temporal Fourier modes. This design enhances the model’s capacity to represent high-frequency dynamical processes, improves long-term prediction stability, and strengthens adherence to underlying physical laws. Experiments demonstrate that FNOtD achieves accuracy comparable to state-of-the-art numerical models on high-resolution ocean forecasting tasks, reduces computational cost by an order of magnitude, and lowers prediction error by over 40% beyond 50 time steps compared to the standard FNO.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Kernel Methods
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Neural operators are becoming the default tools to learn solutions to governing partial differential equations (PDEs) in weather and ocean forecasting applications. Despite early promising achievements, significant challenges remain, including long-term prediction stability and adherence to physical laws, particularly for high-frequency processes. In this paper, we take a step toward addressing these challenges in high-resolution ocean prediction by incorporating temporal Fourier modes, demonstrating how this modification enhances physical fidelity. This study compares the standard Fourier Neural Operator (FNO) with its variant, FNOtD, which has been modified to internalize the dispersion relation while learning the solution operator for ocean PDEs. The results demonstrate that entangling space and time in the training of integral kernels enables the model to capture multiscale wave propagation and effectively learn ocean dynamics. FNOtD substantially improves long-term prediction stability and consistency with underlying physical dynamics in challenging high-frequency settings compared to the standard FNO. It also provides competitive predictive skill relative to a state-of-the-art numerical ocean model, while requiring significantly lower computational cost.

Problem

• Improving long-term prediction stability in ocean dynamics
• Enhancing physical fidelity for high-frequency ocean processes
• Learning dispersion relations while solving ocean governing PDEs

Innovation

• Incorporating temporal Fourier modes enhances physical fidelity
• Entangling space and time captures multiscale wave propagation
• Modified FNOtD internalizes dispersion relation for ocean PDEs