Bilkent University,
Ankara, Turkey

"Neural Network Based Reduced Model for Stokesian Particulate Flows"

Mar 23, 2022 Schedule:

Abstract:

Stokesian particulate flows describe the hydrodynamics of rigid or deformable particlesin the zero Reynolds number regime. Due to highly nonlinear fluid-structure interactiondynamics, moving interfaces, and multiple scales, numerical simulations of such flowsare challenging and expensive. I will present our machine-learning-augmented reducedmodel[1] for fast simulations of such flows. Besides, I will show how the reduced modelenables us study optimal microfluidic device design for dense suspensions of deformableparticles.

Our goal is to design a deterministic lateral displacement (DLD) device to sort same-sizebiological cells by their deformability, in particular to sort red blood cells (RBCs) bytheir viscosity contrast between the fluid in the interior and the exterior of the cells. ADLD device optimized for efficient cell sorting enables rapid medical diagnoses of severaldiseases such as malaria since infected cells are stiffer than their healthy counterparts. Inthis context, I will first describe an integral equation formulation[2] that delivers optimalcomplexity solvers for this type of problems. Despite its excellent theoretical properties,our integral equation solver remains prohibitively expensive for optimization and uncer-tainty quantification. I will then summarize our efforts to reduce the computational costs,starting from low-resolution discretization, domain truncation, and model reduction.

Model reduction is used to accelerate the action of specific and very expensive nonlinearoperators. The final scheme blends ultra low-resolution solvers (who on their own can-not resolve the flow), several regression neural networks, and an operator time-steppingscheme, which we introduced to specifically enable the use of surrogate models. We haveused our methodology successfully for flows that are completely different from the flowsin the training dataset.This is a joint work with George Biros at the University of Texas at Austin.

REFERENCES

• [1] G. Kabacao ̆glu and G. Biros, Machine learning acceleration of simulations of Stoke-sian suspensions.Physical Review E,99, 063313, 201.9
• [2] G. Kabacao ̆glu, B. Quaife, and G. Biros, Low-resolution simulations of vesicle sus-pensions in 2D.Journal of Computational Physics,357, 43-77, 2018.