2024/10/16 by Surbhi Khetrapal, Khetrapal, Surbhi, Jaswin Kasi +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Seismology and Earthquake Studies
paper · pdf · doi:10.48550/arxiv.2410.12280
openalex publication_date 2024/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Solving non-linear partial differential equations which exhibit chaotic dynamics is an important problem with a wide-range of applications such as predicting weather extremes and financial market risk. Fourier neural operators (FNOs) have been shown to be efficient in solving partial differential equations (PDEs). In this work we demonstrate simulation of dynamics in the chaotic regime of the two-dimensional (2d) Kuramoto-Sivashinsky equation using FNOs. Particularly, we analyze the effect of Fourier mode cutoff on the results obtained by using FNOs vs those obtained using traditional PDE solvers. We compare the outputs using metrics such as the 2d power spectrum and the radial power spectrum. In addition we propose the normalised error power spectrum which measures the percentage error in the FNO model outputs. We conclude that FNOs capture the dynamics in the chaotic regime of the 2d K-S equation, provided the Fourier mode cutoff is kept sufficiently high.