Explainable transfer learning for data-driven closure modeling of Rayleigh-Benard turbulence across parameters*

In this work, we develop a data-driven subgrid-scale (SGS) model for large eddy simulation of turbulent thermal convection using a fully convolutional neural network (CNN). With the filtered DNS (FDNS) data, we train the CNN with the filtered state variables, i.e., vorticity, temperature, and stream function as inputs and the nonlinear SGS term (subgrid momentum flux and heat flux) as an output. A-priori analysis shows that the CNN-predicted SGS term accurately captures the inter-scale energy transfer. A-posteriori analysis indicates that the LES-CNN outperforms the physics-based models in both short-term predictions and long-term statistics. Although the CNN-based model is promising in predicting the SGS term, it lacks generalizability to different flow scenarios, e.g., various Rayleigh or Prandtl numbers. To relieve this shortcoming of CNN, here we use the transfer learning (TL) technique which utilizes a previously trained CNN from a base system and a fraction of data (<5%) from a target system. Here we extend the explainable TL framework proposed by our group [1] to guide the TL process in a Fourier-Chebyshev domain with spectral analyses. With proper re-training, a-priori and a-posteriori analyses show that the CNN with TL enhances the SGS model and allows the data-driven model to work stably and accurately in a different flow scenario.

 

References:

[1] Subel, Adam, Yifei Guan, Ashesh Chattopadhyay, and Pedram Hassanzadeh. "Explaining the physics of transfer learning a data-driven subgrid-scale closure to a different turbulent flow." arXiv preprint arXiv:2206.03198 (2022).