Impact and Champions

1. Modeling and Simulation of High Dimensional Stochastic Multiscale PDE Systems at the Exascale IMD Novel Ideas • Development of multi-output Gaussian process model for stochastic problem with discontinuity in the parametric space. • Development of scalable multigrid methods for high dimensional stochastic PDE systems at the exascale. • Development of diffusion map based nonlinear mainifold tools for efficient model reduction of high-dimensional, stochastic multiscale systems. Left column shows the discovered elements. The right column shows the probability density of the observed input points the scheme selects Impact and Champions Milestones/Dates/Status ScheduledActual • Adaptive ANOVA APR 2011 APR 2011 • Multi-output GP SEP 2011 SEP 2011 • Multigrid solver for SPDE APR 2012 APR 2012 • UQ for Carbon Sequestration SEP 2012 SEP 2012 IMPACT. • Efficient multigrid methods can greatly improve the scalability while solving high dimensional SPDE systems at the exascale. • Multi-output Gaussian process model can be used as a surrogate model for high-dimensional SPDE solver for fault detection and fault resilience. • Scalable UQ solvers enable us to do predictive modeling of carbon sequestration with high dimensional randomly heterogeneous permeability field. Principal Investigator(s):G. Lin PNNL, N. Zabaras Cornell Univ., I. KevrekidisPrinceton Univ. March 30, 2012