Current Projects

Uncertainty propagation in multiscale/multiphysics materials systems

Computational techniques for polycrystalline materials-by-design with an integration of multiscale modeling and statistical learning

First principles calculations for the design of materials with extremal properties

Computational and mathematical aspects of stochastic multiscale continuum systems: Stochastic input representation and model reduction, model reduction of SPDE systems, data-driven manifold learning, solution and optimization of SPDE systems in high-dimensions, etc.

Bayesian inference, inverse problems, multiscale estimation

Fluid flow and transport phenomena in random heterogeneous media, geological, environmental and energy applications

Multiscale models of microstructure evolution using level set and phase field methods