Velocity gradient prediction using parameterized Lagrangian deformation models

We seek to efficiently predict the statistical evolution of the velocity gradient tensor (VGT) by creating local models for the pressure Hessian. Previous work has identified physics-informed machine learning (PIML) to be adept in this prediction; of note in this class of models is the Tensor Basis Neural Network (TBNN) for its embedded physical constraints and demonstrated performance. Simultaneously, phenomenological models were advanced by approximating the local closure to the pressure Hessian via deformation models using the history of the VGT. The latest in this series of models is the Recent Deformation of Gaussian Fields (RDGF) model. In this work, we combine the (local in time) PIML approach with the phenomenological idea of inclusion of recent deformation to create a data-driven Lagrangian deformation model. We compare the model performance to both the TBNN and the RDGF models, and provide data-driven hypotheses regarding the upstream assumptions made in the RDGF model.