Reduced-order modeling of a viscoelastic turbulent jet with hybrid machine learning models

Abstract

Adding flexible polymers to a Newtonian solvent confers complex properties to the resulting solution. The additional complexity substantially increases the computational cost of numerical simulations, which often makes them prohibitively expensive. Here, we propose hybrid reduced-order models to accelerate simulations of viscoelastic turbulent jets. The model combines modal decompositions with deep networks: we use proper orthogonal decomposition to obtain a compact representation of the data, and a neural network is trained to predict the mode coefficients in the low-dimensional space. Results show that the hybrid model effectively captures the long-term behavior of the viscoelastic jet, that we demonstrate by computing relevant statistics of the jet. While small models are capable of predicting large-scale dynamics more than one-step at a time, thus facilitating greater accelerations, larger models are mandatory for forecasting smaller-scale dynamics, with skip connections the most effective strategy for deeper and generalizable models. The proposed methodology underpins the potential of hybrid approaches for compact and robust reduced-order models of viscoelastic turbulent jets.