Modeling turbulent and self-gravitating fluids with Fourier neural operators

Abstract: Neural Operators (NOs) are a leading method for surrogate modeling of partial differential equations. Unlike traditional neural networks, which approximate individual functions, NOs learn the mappings between function spaces. While NOs have been predominantly tested on simplified 1D and 2D problems, such as those explored in prior works, these studies fail to address the complexities of more realistic, high-dimensional, and high-dynamic range systems. Moreover, many real-world applications involve incomplete or noisy data, which has not been adequately explored in current NO literature. In this work, we present a novel application of NOs to astrophysical data, which involves high-dynamic range projections into an observational space. We train Fourier NO (FNO) models to predict the evolution of incomplete observational proxies with density variations spanning four orders of magnitude. We demonstrate that FNOs can predict the effects of unobserved dynamical variables. Our work lays the groundwork for future studies that forecast direct astronomical observables.