Solving Navier-Stokes Equations with Deep Learning Solvers for Ocean Phenomena Simulation

The simulation of oceanic phenomena plays a pivotal role in understanding and predicting climate change, as well as in protecting marine ecosystems, sustainable utilization of marine resources, and effective disaster prevention and mitigation. These simulations are typically based on the Navier-Stokes equations; however, traditional numerical solutions are computationally expensive and present numerous challenges. With the advancement of deep learning technology, the application of Physics-Informed Neural Networks (PINNs) to solve the Navier-Stokes equations has become a burgeoning field, promising significant improvements in computational efficiency. However, existing methods are heavily dependent on extensive fluid model data and suffer from limited generalizability. To overcome these limitations, this paper proposes a novel, self-supervised, and highly generalizable numerical solution method for the Navier-Stokes equations. This method integrates convolutional neural networks under physical supervision, thereby allowing the equation to be solved and a variety of oceanic phenomena to be simulated without resorting to traditional fluid simulation data. Our experimental results indicate that this method can efficiently and effectively simulate oceanic phenomena under various environmental conditions, with its validity corroborated by alignment with observations from the SDGSAT-1 satellite. This study offers an efficient and innovative tool for the simulation and analysis of oceanic phenomena, thereby contributing significantly to climate research and marine resource management.