Multi-Scale Fusion of Information for Uncertainty Quantification and Management in Large-Scale Simulations
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).
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 02, 2015
- Accession Number
- AD1000736
Entities
People
- George Karniadakis
Organizations
- Brown University