Improving Predicted Statistics of Velocity Gradient Closures using Parameterized Lagrangian Deformation Models

We advance the modeling of the statistical evolution of the velocity gradient tensor in isotropic turbulence by incorporating parameterized Lagrangian memory terms into a physics-informed machine learning framework. Our novel approach synergizes data-driven techniques from the previously proposed Tensor Basis Neural Network (TBNN) model with phenomenological deformation theories, such as the recent Fluid Deformation Models (FDM). This new model, termed the Lagrangian Deformation Tensor Network, outperforms both the TBNN and phenomenological models in predictive capability while elucidating Lagrangian memory effects. The learned memory kernels are analyzed and compared to the results obtained from the alternative Mori-Zwanzig representation of memory effects and the phenomenological upstream assumptions in the FDMs. Our findings highlight the significant role of time-history in predicting the deviatoric pressure Hessian.