About this Group

About

The thrust of the research of the CRUNCH group is the development of data-driven stochastic multiscale methods for physical and biological applications, specifically numerical algorithms, visualization methods and parallel software for continuum and atomistic simulations in biophysics, soft matter and functional materials, fluid and solid mechanics, biomedicine and related applications. Machine learning in Scientific Computing is a new (disruptive) area that we emphasize, i.e., encoding conervation laws into kernels to build Physics-informed Learning Machines. Numerical methods developed at CRUNCH are spectral/hp element methods, multi-element polynomial chaos, stochastic molecular dynamics (DPD), and spectral and high-order methods for fractional partial differential equations. The CRUNCH group has pioneered such methods, e.g. the spectral element method on unstructured meshes (1995), generalized polynomial chaos (gPC) for uncertainty quantification, rigorous coarse grained molecular methods (2010), and poly-fractonomials for fractional operators (2015). More recently we have focused on numerical Gaussian Processes that allow us to solve PDEs from noisy measurements only without the tyranny of building elaborate grids! In particular, we are interested to employ fractional operators and Gaussian processes to discover hidden physics models -- our group has pionerred this! Funding is currently provided by DOE, AFOSR, DARPA, ARO, ARL, NIH and NSF.