Clifford Neural Operators on Atmospheric Data Influenced Partial Differential Equations

Abstract

Mathematical representations of the atmosphere are key to forecasting and research tasks across Earth science. Numerically solving the underlying partial differential equations (PDEs) of the atmosphere, however, can be difficult and computationally expensive with numerous trade-offs between computing efficiency and accuracy. Utilizing neural networks to learn approximations of the PDE solutions from the data can help us model complex phenomena more efficiently than traditional numerical schemes. Here, we have applied Clifford algebra-based neural operators for predicting atmospheric variables. Clifford Fourier neural operators are used with two different backbone architectures, ResNet and UNet, on custom data of U10, V10 and surface pressure as well as U500, V500 and Z500. Clifford Fourier neural operators, coupled with ResNet and UNet architectures, are applied to a key reanalysis dataset. Model performance is initially strong, but we observe increasing errors, resulting in the model becoming highly unstable.