Accession Number : AD1000736

Title :   Multi-Scale Fusion of Information for Uncertainty Quantification and Management in Large-Scale Simulations

Descriptive Note : Technical Report,01 Sep 2009,31 Aug 2015

Corporate Author : Brown University, Providence Providence

Personal Author(s) : Karniadakis,George E

Full Text :

Report Date : 02 Dec 2015

Pagination or Media Count : 28

Abstract : We developed an integrated methodology for uncertainty quantification (UQ) that proceedsfrom initial problem definition to engineering applications. Towards this goal, we worked onfive research areas: (1) Mathematical analysis of SPDEs and multiscale formulation; (2) Nu-merical solution of SPDEs; (3) Reduced-Order modeling; (4) Estimation/Inverse problems; and(5) Robust optimization and control. This work set the mathematical foundations of Uncer-tainty Qantification methods used by many diverse communities in computational mechanics,fluid dynamics, plasma dynamics, and materials science. We have pioneered methods for efficienthigh-dimensional representations of stochastic processes, established Wick-Malliavin approxima-tion for nonlinear SPDEs, theoretical error estimates for multiscale parametric and stochasticPDEs, a new approach to design of experiment and UQ on parametric manifolds, multi-fidelityoptimization-under-uncertainty, a data-driven Bayasian framework and probabilistic graphicalmodels for UQ, and information-based coarse graining methods. We have also demonstratedan integration of our UQ methodology and all five areas for a benchmark problem. We havepublished more than 150 papers in top mathematical journals, obtained one patent (MIT),and have established one software company (MIT).

Descriptors :   simulation , engineering , mathematical analysis , stochastic processes , models , optimization , mechanics , fluid dynamics , materials science , estimates , theory , data fusion

Subject Categories : Numerical Mathematics
      Information Science
      Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE