Long-term predictions of turbulence by implicit U-Net enhanced Fourier neural operator

Abstract

Long-term predictions of nonlinear dynamics of three-dimensional (3D) turbulence are very challenging for machine learning approaches. In this paper, we propose an implicit U-Net enhanced Fourier neural operator (IU-FNO) for stable and efficient predictions on the long-term large-scale dynamics of turbulence. The IU-FNO model employs implicit recurrent Fourier layers for deeper network extension and incorporates the U-net network for the accurate prediction on small-scale flow structures. The model is systematically tested in large-eddy simulations of three types of 3D turbulence, including forced homogeneous isotropic turbulence (HIT), temporally evolving turbulent mixing layer, and decaying homogeneous isotropic turbulence. The numerical simulations demonstrate that the IU-FNO model is more accurate than other FNO-based models including vanilla FNO, implicit FNO (IFNO) and U-Net enhanced FNO (U-FNO), and dynamic Smagorinsky model (DSM) in predicting a variety of statistics including the velocity spectrum, probability density functions (PDFs) of vorticity and velocity increments, and instantaneous spatial structures of flow field. Moreover, IU-FNO improves long-term stable predictions, which has not been achieved by the previous versions of FNO. Besides, the proposed model is much faster than traditional LES with DSM model, and can be well generalized to the situations of higher Taylor-Reynolds numbers and unseen flow regime of decaying turbulence.

45 pages, 21 figures

References in corpus (20)

• Fourier Neural Operator for Parametric Partial Differential Equations
• FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators
• Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow
• Physics-Informed Neural Operator for Learning Partial Differential Equations
• Recent advances in applying deep reinforcement learning for flow control: perspectives and future directions
• Theory-guided hard constraint projection (HCP): a knowledge-based data-driven scientific machine learning method
• Deep transfer operator learning for partial differential equations under conditional shift
• Stable a posteriori LES of 2D turbulence using convolutional neural networks: Backscattering analysis and generalization to higher Re via transfer learning
• Attention-Enhanced Neural Network Models for Turbulence Simulation
• Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network
• GNOT: A General Neural Operator Transformer for Operator Learning
• U-net architectures for fast prediction of incompressible laminar flows
• On universal approximation and error bounds for Fourier Neural Operators
• Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers
• A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows
• Magnetohydrodynamics with Physics Informed Neural Operators
• Dimension Reduced Turbulent Flow Data From Deep Vector Quantizers
• An exploratory study on machine learning to couple numerical solutions of partial differential equations
• Forecasting subcritical cylinder wakes with Fourier Neural Operators
• Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation

Cited by in corpus (9)

• Fourier Neural Operator Surrogate Model to Predict 3D Seismic Waves Propagation
• A Mathematical Guide to Operator Learning
• Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone
• Machine learning-based vorticity evolution and superresolution of homogeneous isotropic turbulence using wavelet projection
• Residual U-Net for accurate and efficient prediction of hemodynamics in two-dimensional asymmetric stenosis
• Machine-learning-based simulation of turbulent flows over periodic hills using a hybrid U-Net and Fourier neural operator framework
• Banach neural operator for Navier-Stokes equations
• Evaluation of Deep Neural Operator Models toward Ocean Forecasting
• Uncertainty quantification and stability of neural operators for prediction of three-dimensional turbulence