Research

Physics-informed Deep Learning

Inspired by recent developments in physics-informed deep learning, I have been able to leverage the hidden physics of fluid mechanics (i.e. the Navier-Stokes equations) and infer the latent quantities of interest (e.g. the velocity and pressure fields) by assimilating data from visualizations of a passive scalar, which offers a promising alternative to the conventional methods. Here, the passive scalar could be the bolus dye that is typically injected to the blood stream for the purpose of blood flow monitoring and medical imaging. The videos show the inferred velocity and pressure fields using numerically generated input data on the passive scalar.

Data-driven Multiscale Modeling of Biological Processes

The study of the pathogenesis and progression of aneurysms has become a multidisciplinary effort involving a wide range of areas spanning from molecular and cell biology to solid and fluid mechanics. It is also a multiscale problem in nature as spatial variations occur at scales from centimeters at the organ level to micro/nanometers at the cellular and subcellular level, while the temporal scales range from microseconds to days and weeks in the case of thrombus formation and aortic wall remodeling. I proposed a multiscale numerical framework that specifically aims to address both spatial and time-scale problem in such processes. The multiscale numerical method we proposed here is novel in that it tackles both short-term and long-term processes. Clearly, the challenge in this problem is long-term simulation of thrombus actively coupled with blood flow.