nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling

Mahmoudabadbozchelou, Mohammadamin; Karniadakis, George Em.; Jamali, Safa

doi:10.1039/d1sm01298c

nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling

Journal Article · Thu Nov 18 00:00:00 EST 2021 · Soft Matter

DOI:https://doi.org/10.1039/d1sm01298c· OSTI ID:1978828

^[1]; Karniadakis, George Em. ^[2]; ^[3]

Northeastern Univ., Boston, MA (United States); OSTI
Brown Univ., Providence, RI (United States)
Northeastern Univ., Boston, MA (United States)

Time- and rate-dependent material functions in non-Newtonian fluids in response to different deformation fields pose a challenge in integrating different constitutive models into conventional computational fluid dynamic platforms. Considering their relevance in many industrial and natural settings alike, robust data-driven frameworks that enable accurate modeling of these complex fluids are of great interest. The main goal is to solve the coupled Partial Differential Equations (PDEs) consisting of the constitutive equations that relate the shear stress to the deformation and fully capture the behavior of the fluid under various flow protocols with different boundary conditions. Here, in this work, we present non-Newtonian physics-informed neural networks (nn-PINNs) for solving systems of coupled PDEs adopted for complex fluid flow modeling. The proposed nn-PINN method is employed to solve the constitutive models in conjunction with conservation of mass and momentum by benefiting from Automatic Differentiation (AD) in neural networks, hence avoiding the mesh generation step. nn-PINNs are tested for a number of different complex fluids with different constitutive models and for several flow protocols. These include a range of Generalized Newtonian Fluid (GNF) empirical constitutive models, as well as some phenomenological models with memory effects and thixotropic timescales. nn-PINNs are found to obtain the correct solution of complex fluids in spatiotemporal domains with good accuracy compared to the ground truth solution. We also present applications of nn-PINNs for complex fluid modeling problems with unknown boundary conditions on the surface, and show that our approach can successfully recover the velocity and stress fields across the domain, including the boundaries, given some sparse velocity measurements.

View Accepted Manuscript (DOE)

Research Organization:: Brown Univ., Providence, RI (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0019453

OSTI ID:: 1978828

Alternate ID(s):: OSTI ID: 1833444

Journal Information:: Soft Matter, Journal Name: Soft Matter Journal Issue: 1 Vol. 18; ISSN 1744-683X

Publisher:: Royal Society of ChemistryCopyright Statement

Country of Publication:: United States

Language:: English

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