Uncertainty quantification on constrained spaces

Constrained spaces are ubiquitous in computational engineering: random variables and random fields modeling physical variables typically take values in sets defined by inequality constraints, and index sets can present themselves as manifolds. In this context, stochastic modeling for uncertainty quantification becomes a challenging task that must account for mathematical admissibility, physical consistency, and identifiability conditions. In this talk, we will present recent advances on the modeling of non-Gaussian random fields on constrained domains and state spaces. The approach builds upon the combination of information-theoretic transport maps and stochastic partial differential equations. Various applications will be presented, including nonlinear simulations on patient-specific brain and artery geometries, multiscale computations, and inverse problems on structures produced by additive manufacturing.
Zoom link: https://duke.zoom.us/j/98047568506?pwd=WXcxaENrUnZjS010c2xuYWFLTVNWQT09