Rheology-informed neural networks for non-local granular flows

Constitutive equations describing the rheology of complex fluids commonly construct relationships between the stress tensor at a given location and its dependence on the shear rate at the very same location; however, it is now well understood that in some complex systems, the stress response of a fluid element also depends on the length scales far beyond its immediate neighborhood. For instance, the existence of non-vanishing creeping flows in regions below the yield stress threshold and the dependence of the yield stress on the thickness of the deposited granular matter cannot be accurately described by local rheology. These have resulted in the development of a non-local rheology framework relevant to a wide range of applications with inevitable challenges in its model development and verification. To alleviate these challenges and get the most from relatively scarce experimental data, we developed rheology-informed neural networks (RhiNNs) platforms to describe the non-local rheology of granular flows effectively. By introducing physical intuitions into the existing data-driven approaches usually uninformed of the physical domain, we wish to capture the non-locality of granular flows by solving their constitutive equations, which are demanding to tackle through numerical methods or may even be misleading with locality assumptions or simple Deep Neural Networks (DNNs). Here, in the forward problem, the existing non-local constitutive equations with appropriate boundary and initial conditions are used to solve the stress field. In the inverse problem, though, limited sample data are fed into RhiNN to pinpoint the unknown parameters of underlying assumed constitutive equations. The combination of the forward and inverse problems in RhiNNs may shed light on the rather tricky nature of non-local rheology of granular flows and provide the community with a versatile, easy-to-use alternative to computationally expensive numerical frameworks.