LESnets (Large-Eddy Simulation nets): Physics-informed neural operator for large-eddy simulation of turbulence

Acquisition of large datasets for three-dimensional (3D) partial differential equations (PDE) is usually very expensive. Physics-informed neural operator (PINO) eliminates the high costs associated with generation of training datasets, and shows great potential in a variety of partial differential equations. In this work, we employ physics-informed neural operator, encoding the large-eddy simulation (LES) equations directly into the neural operator for simulating three-dimensional incompressible turbulent flows. We develop the LESnets (Large-Eddy Simulation nets) by adding large-eddy simulation equations to two different data-driven models, including Fourier neural operator (FNO) and implicit Fourier neural operator (IFNO) without using label data. Notably, by leveraging only PDE constraints to learn the spatio-temporal dynamics, LESnets models retain the computational efficiency of data-driven approaches while obviating the necessity for data. Meanwhile, using LES equations as PDE constraints makes it possible to efficiently predict complex turbulence at coarse grids. We investigate the performance of the LESnets models with two standard three-dimensional turbulent flows: decaying homogeneous isotropic turbulence and temporally evolving turbulent mixing layer. In the numerical experiments, the LESnets models show similar accuracy as compared to traditional large-eddy simulation and data-driven models including FNO and IFNO, and exhibits a robust generalization ability to unseen regime of flow fields. By integrating a single set of flow data, the LESnets models can automatically learn the coefficient of the subgrid scale (SGS) model during the training of the neural operator. Moreover, the well-trained LESnets models are significantly faster than traditional LES, and exhibits comparable computational efficiency to the data-driven FNO and IFNO models.