Applicability of Machine Learning Methodologies to Model the Statistical Evolution of the Coarse-Grained Velocity Gradient Tensor

The evolution of the Lagrangian velocity gradient tensor contains local information about a variety of important turbulence characteristics. Work to model this evolution in isotropic turbulence, and at the smallest scales, has been successful - particularly through the use of machine learning (ML) techniques to approximate local closures to the non-local pressure hessian. However, extension of these methods to describe the evolution of the velocity gradient tensor (CGVGT) coarse-grained at a scale within the inertial range of turbulence remains to be a challenge. In this work, we examine the statistics of the CGVGT and its associated pressure Hessian to determine why the proposed ML methods struggle as the coarse-graining size increases. Through this investigation, we hope to enable a path forward in modeling the statistical evolution of the CGVGT.