mlsanityData to 13 Oct 2026

A Numerical Study of Chaotic Dynamics of K-S Equation with FNOs

arXiv 2410.12280 ↗First posted 16 Oct 2024cs.LG nlin.CDcited by 1

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Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 13 Oct 2026). Builds on 10 of its 18 references that are in the map. First posted on arXiv 16 Oct 2024.

Builds on

10 of 18 references.

References · 10

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,857
  2. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 766
  3. 2019DeepXDE: A deep learning library for solving differential equationscited by 618
  4. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 604
  5. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 422
  6. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 299
  7. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 212
  8. 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
  9. 2022A Multi-Scale Deep Learning Framework for Projecting Weather Extremescited by 7
  10. 2024Fourier Neural Operators for Learning Dynamics in Quantum Spin Systemscited by 2

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Cited by year

Citing papers per year: 2025: 1.

1 paper.

  1. 2025Meta-Learning Fourier Neural Operators for Hessian Inversion and Enhanced Variational Data Assimilationcited by 0