On-the-fly Learning

We simulate complex fluids by means of an on-the-fly coupling of the bulk rheology to the underlying microstructure dynamics.In particular, a continuum model of polymeric fluids is constructed without a pre-specified constitutive relation, but instead it isactively learned from mesoscopic simulations where the dynamics of polymer chains is explicitly computed. To couple the bulkrheology of polymeric fluids and the microscale dynamics of polymer chains, the continuum approach (based on the finite volumemethod) provides the transient flow field as inputs for the (mesoscopic) dissipative particle dynamics (DPD), and in turn DPDreturns an effective constitutive relation to close the continuum equations. In this multiscale modeling procedure, we employan 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 flowpast a circular cylinder of a non-Newtonian fluid, modeled at the mesoscopic level by bead-spring chains. The results show thatonly 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 methoddemonstrated here obtains only a local viscosity from the polymer dynamics, it can be extended to other multiscale models ofcomplex fluids whose macro-rheology is unknown.

Lifei Zhao,  Zhen Li,  Bruce Caswell,  Jie Ouyang,  George Em Karniadakis, Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flowsarXiv:1709.06228