Research Theme

Our research focuses on the development of theoretical and computational models of multiscale, multiphysics problems, with special emphasis on geomechanics applications, such as geological carbon sequestration, hydraulic fracture, and nuclear waste disposal. In particular, we are interested at developing both theories and numerical algorithms to predict how multiphase solids react to diverse influences such as stress, deformation, heat source, presence of chemical species and fluid flows, and how material instabilities such as strain localization, soil liquefaction, and fractures occur and propagate across different spatial and temporal scales. 

Our current research at Columbia University encompasses the following interconnected areas:

• Meta-modeling game with deep reinforcement learning for constraint-compatible modelings. 
• Applications of knowledge graph for interpretable predictions, generative mathematical logics and adversarial attacks for constitutive laws. 
• Non-Euclidean descriptors for microstructural-informed material modelings.   ​
• Micromechanics of porous media and granular physics.
• Computational plasticity for porous and granular materials exposed to extreme environments. 
• Concurrent and homogenized-based multiscale multiphysics modeling in various spatial and temporal scales.  
• Stable and consistent mixed finite element formulations for fully coupled multi-physics problems.
• Higher-order continua and the corresponding homogenization theory for porous media. 
• Development of computer models and analytical tools for modern applications in the fields of offshore, nuclear, dam, mining and transportation engineering.