Physics-informed Machine Learning for Reduced-order Modeling of Lagrangian Turbulence

Fully resolving turbulent flows in physical sciences and engineering applications using Direct Numerical Simulation (DNS) is generally prohibitively expensive due to the wide range of scales and their non-linear interactions. This challenge has motivated the development of efficient reduced-order models of turbulence dynamics, which has seen a remarkable new boost from disparate fields of Machine Learning. The talk represents an overview of our efforts in developing reduced-order models describing various aspects of Lagrangian turbulent dynamics under the Physics-Informed Machine Learning (PIML) paradigm. We inject physical constraints into the construction of Neural Network models for turbulence dynamics at both coarse-grained scale (based on Smoothed Particle Hydrodynamics) and Kolmogorov scale (based on Velocity Gradient Tensor dynamics). A large Lagrangian dataset is extracted from high-Reynolds number DNS and used to train the PIML models. Through a series of diagnostic tests, we show that the trained PIML models are capable of producing the correct flow structures and turbulence statistics in homogeneous isotropic turbulence. In addition, the Lagrangian framework shows good promise for extrapolating the PIML models outside the training data, e.g. to higher Reynolds numbers.