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

A new paradigm in using machine learning methods for multiscale modeling of non-Newtonian fluids by means of an on-the-fly coupling of the bulk rheology to the underlying microstructure dynamics, where 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. The continuum solver provides the transient flow field as inputs for the mesoscopic simulator, and in turn mesoscopic dynamics returns an effective constitutive relation to close the continuum equations. Active learning scheme is developed to adaptively initiate mesoscopic simulations only as necessary for new training points, so that only a few expensive runs are required to construct an effective constitutive closure for the macroscopic solver.