Learning the constitutive relation of polymeric flows with memory

TL;DR

This paper introduces a data-driven method using Gaussian Process regression to learn the stress constitutive relation in polymeric flows with memory, enabling accurate macroscopic flow simulations without assuming a specific functional form.

Contribution

The authors develop a novel learning approach that infers constitutive relations directly from microscopic simulations, generalizable to complex soft matter systems with hierarchical scales.

Findings

Learned constitutive relations match multi-scale simulation results.

Method captures flow history dependence and elastic effects.

Applicable to various soft matter systems with hierarchical dynamics.

Abstract

We develop a learning strategy to infer the constitutive relation for the stress of polymeric flows with memory. We make no assumptions regarding the functional form of the constitutive relations, except that they should be expressible in differential form as a function of the local stress- and strain-rate tensors. In particular, we use a Gaussian Process regression to infer the constitutive relations from stress trajectories generated from small-scale (fixed strain-rate) microscopic polymer simulations. For simplicity, a Hookean dumbbell representation is used as a microscopic model, but the method itself can be generalized to incorporate more realistic descriptions. The learned constitutive relation is then used to perform macroscopic flow simulations, allowing us to update the stress distribution in the fluid in a manner that accounts for the microscopic polymer dynamics. The results using the learned constitutive relation are in excellent agreement with full Multi-Scale Simulations, which directly couple micro/macro degrees of freedom, as well as the exact analytical solution given by the Maxwell constitutive relation. We are able to fully capture the history dependence of the flow, as well as the elastic effects in the fluid. We expect the proposed learning/simulation approach to be used not only to study the dynamics of entangled polymer flows, but also for the complex dynamics of other Soft Matter systems, which possess a similar hierarchy of length- and time-scales.