Polyscrystalline materials are composed of many tiny sigle crystal pieces (known as grains) stuck together. It is common microstructure for metals and ceramics. The growth of grain boundaries are of interest because important physical properties (e.g., yield strength, conductivity, etc.) of polycrystalline material depend on the grain boundaries, arising industrial process such as heat treatment (annealing). If one can model and simulate the growth of grainboundaries accurately, polycrystalline materials can be tuned to achieve a variety of uses.

I use machine-learning techniques to solve an elliptic partial differential equation, which typically arises for modeling creeping non-Newtonian fluid flows. In mechanics of non-Newtonian fluid, (often called as computaitonal rheology) the complicated rheological behavior of fluids induces strong non-linearities of the governing equation. Resolving exponential solution profile with a conventional numerical method still remains a challening task. Instead, I take a turn to neural network approach for solving such systems. Rheolgical model provides a vast amount of prior knowledge that may have not been fully exploited. To make the best use of it, physically informed neural network (PINN) transforms clascial mechanic problem into typical minimization problems and train deep neural network to solve supervised learning tasks. This process respects the physics described by constitutive equation of Non-Newtonian models. While the PINN framework is yet premature compared to classcial numerical methods, its potential capability to predict the strong non-linear behavior of a material deserves intensive future research in this field.

I use Finite-element method to simulate non-Newtonian fluid flows. I consider fluid mechanics of rheologically complex fluids with yield stress, viscoelasticity, and thixotropy. While there exist a variety of rheological models to describe these nonlinear fluid-mechanics, parameters of the models are usually fit against data acquired from simplest geometry. Therefore, the uses of rheological models for real material process stage, which often include involved flow geometry, are inherently extrapolative. I consider the uncertainty quantificaiton of such cases and investigate the sensitivity of model parameters in simulation predictions.