My research interests lie in applied mathematics and scientific computing, in particular, multi-scale modeling with applications to fluid physics, materials science, and biophysics. The research goal is to establish accurate modeling of multi-scale systems relevant to meso-scale transport, non-Newtonian hydrodynamics, and kinetic transport processes arising from various science and engineering applications. For such problems, the multi-scale and high-dimensional nature imposes a fundamental challenge; empirical models based on ad-hoc closure assumptions often show limitations. Currently, my group is devoted to constructing machine-learning based models for such systems directly from the first-principle-based descriptions. In particular, we focus on developing numerical methods to learn reliable and numerically-stable models that faithfully entail the micro-scale interactions, retain physical interpretation, and respect physical constraints. The long-term goal is to achieve predictive modeling of these multi-scale systems beyond phenomenologically understanding and establish integrated control across multiple scales.

• Machine learning methods for multi-scale modeling
• Model reduction and stochastic simulation
• Scientific machine-learning
• Fluid physics

We are grateful for grant support from NSF, DOE, Ford, and MSU Foundation.