A multiscale computational framework using active learning to model complex suspension flows

Abstract

We devise a novel computational framework to achieve efficient multiscale modeling for suspension flows. The modeling framework comprises a particle-resolving direct numerical simulation for microscopic computation, a single-fluid continuum model to capture the bulk flow behavior at the macroscale, and a Gaussian process regression that connects the two modeling components. The microscopic calculation simulates detailed flow fields around individual suspended particles. Along with a coarse-grained method, we are able to obtain the mean volume fractions and stresses for discrete particles, which are then further used to calculate the rheological properties of the bulk flow fields at the macroscale under specific forcing conditions. Using Gaussian process regression, a few data points from the microscopic calculations can be further interpolated/extrapolated to form complete constitutive relationships that cover the whole forcing range in macroscopic calculations (i.e., continuum modeling). Moreover, via the uncertainties returned from the Gaussian process regression, the resulting active learning strategy using the Gaussian process regression automatically decides on the required the microscopic calculations given by a specified tolerance. As a result, complex suspension problems can be efficiently solved by the macroscopic continuum model to the desired accuracy with the minimum computational effort (i.e., minimum number of microscopic runs). Four examples are demonstrated, among which two examples involve particle migration as a function of the particle stress, and the resulting nonuniform distribution of particles. This demands a multivariate Gaussian process regression, which is found to be particularly effective in achieving high computational efficiency compared with the off-line cases, i.e., a large number of off-line microscopic calculations to obtain the prescribed constitutive relationships.