Machine-learned constitutive relations for multi-scale simulations of well-entangled polymer melts

Abstract

We investigate the use of a machine-learning-based simulation scheme to predict flows of complex fluids with a non-linear constitutive relation. This scheme, originally proposed by Seryo et al. for general complex fluids [N. Seryo et al., “Learning the constitutive relation of polymeric flows with memory,” Phys. Rev. Res. 2, 033107 (2020)], is used to learn the time derivative of the stress as a function of the stress and velocity gradient. However, previous assessments were limited to fluids with linear constitutive relations. In this study, we employ the dual sliplink model to express the dynamics of well-entangled polymers as a fluid exhibiting a non-linear stress response. We test the simulation scheme by using it to predict the flow of a viscoelastic fluid between two parallel plates with only shear deformations and compare the results with those of a multi-scale simulation using microscopic simulators. Overall, our machine-learning method possesses good predictive capabilities, for both the transient response and the non-linear behavior at steady-state, i.e., the shear-thinning. We are able to accurately track the evolution of the stress, for both the weak and strong elastic cases, although the velocity predictions for the latter show a decreased accuracy in the transient regime. Furthermore, our simulation scheme is more computationally efficient than the conventional multi-scale simulation approach, which uses microscopic simulators, containing a system of coarse-grained polymers, to evaluate the macroscopic stress. We discuss possible extensions and improvements for enhancing the predictive capabilities and generality of the method.