Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows

TL;DR

This paper introduces an active learning multiscale modeling approach that efficiently couples macroscopic flow simulations with mesoscopic polymer dynamics, reducing the number of costly DPD simulations needed for non-Newtonian fluid modeling.

Contribution

It develops an active learning framework using Gaussian process regression to adaptively select DPD simulations, enabling efficient and accurate multiscale modeling of complex fluids without pre-defined constitutive relations.

Findings

Only five DPD simulations needed at Re=10

One additional DPD simulation extends the model at Re=100

Active learning significantly improves computational efficiency

Abstract

We simulate complex fluids by means of an on-the-fly coupling of the bulk rheology to the underlying microstructure dynamics. In particular, a macroscopic continuum model of polymeric fluids is constructed without a pre-specified constitutive relation, but instead it is actively learned from mesoscopic simulations where the dynamics of polymer chains is explicitly computed. To couple the macroscopic rheology of polymeric fluids and the microscale dynamics of polymer chains, the continuum approach (based on the finite volume method) provides the transient flow field as inputs for the (mesoscopic) dissipative particle dynamics (DPD), and in turn DPD returns an effective constitutive relation to close the continuum equations. In this multiscale modeling procedure, we employ an active learning strategy based on Gaussian process regression (GPR) to minimize the number of expensive DPD simulations, where adaptively selected DPD simulations are performed only as necessary. Numerical experiments are carried out for flow past a circular cylinder of a non-Newtonian fluid, modeled at the mesoscopic level by bead-spring chains. The results show that only five DPD simulations are required to achieve an effective closure of the continuum equations at Reynolds number Re=10. Furthermore, when Re is increased to 100, only one additional DPD simulation is required for constructing an extended GPR-informed model closure. Compared to traditional message-passing multiscale approaches, applying an active learning scheme to multiscale modeling of non-Newtonian fluids can significantly increase the computational efficiency. Although the method demonstrated here obtains only a local viscosity from the mesoscopic model, it can be extended to other multiscale models of complex fluids whose macro-rheology is unknown.