Application of machine-learned constitutive relations for well-entangled polymer melt flows*

We investigated the effectiveness of a Machine Learning (ML) approach to learn the constitutive relation of well-entangled polymer melts. In particular, we use a Gaussian Process regression on training data (e.g., stress, strain rate, number of entanglements) obtained from microscopic Slip-link simulation under various flow conditions. The learned constitutive relations (given in differential form) were then used within macroscopic Smooth Particle Hydrodynamics simulations of standard flows (i.e., parallel plates and contraction expansion).

Compared to currently used hierarchical simulation methods, which directly couple the microscopic polymer dynamics and the macroscopic flows, our method is ~100 times faster and drastically reduces the statistical fluctuations in the flow predictions, while maintaining a clear connection to the underlying molecular model. In this presentation, we will use benchmark Multi-Scale simulation results to present a detailed error analysis of our ML predictions and their computational efficiency. 

This work was partially supported by Japan Society for the Promotion of Science Kakenhi (19H01862, 20K037865), SPIRITS 2020 of Kyoto University, Ogasawara Foundation.