Neural Network Surrogates for Weather Prediction Using Numerical Solutions of the Shallow Water Equations
Keywords:
Surrogates for Neural Networks, Weather Forecasting, Shallow Water Equations, Physics-Informed Neural Networks (PINNs), Numerical Methods, ERA5 Dataset, Computational Fluid Dynamics, and Finite Difference Solvers are some of the topics that are covered in this article.Abstract
Combining numerical solvers that are based on physics with architectures that are based on machine learning opens up a new computational frontier for enhancing the accuracy of weather forecasting. The purpose of this study is to examine the use of neural network surrogates for the purpose of estimating numerical solutions to the shallow water equations (SWEs), which serve as the foundation for a great number of models that apply to the atmosphere and the ocean. These equations, which are derived from the Navier-Stokes equations and the hydrostatic balancing assumption, are used extensively in large-scale geophysical fluid dynamics, with a special emphasis on weather forecasting. On the other hand, its numerical solution is reliant on resolution and requires a significant amount of processing resources. This study proposes the development of a physics-informed neural network (PINN) surrogate model that is trained on high-resolution simulation data in order to simulate numerical solvers of the SWEs that are subject to physical constraints: this is done in order to alleviate the problem. A comparison is made between the surrogate model and classical finite-difference time-domain (FDTD) numerical solutions in terms of generalizability, computing efficiency, and accuracy. The comparison is made using authenticated NOAA and ECMWF ERA5 reanalysis datasets. According to the findings, the surrogate model is able to cut down on computing time by more than 80 percent without affecting accuracy, with the Root Mean Square Error (RMSE) for normalized variables remaining within a range of 0.07. Additionally, the neural surrogate is able to maintain the important time-scale information of wave propagation and vortices structures, which demonstrates its potential to revolutionize the numerical weather prediction (NWP) systems.
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