RESEARCH

Research Objectives

Uncertainty Quantification (UQ) is important to the USAF for the development of methods in electromagentic scattering, materials, flow-structure interaction, aero-acoustics, and the preliminary design of revolutionary vehicles. 

Uncertainty sources can include

• initial/boundary conditions, material properties, constitutive laws, and geometry
• limited noisy experimental data
• lack of knowledge
• inherent randomness of the underlying physical phenomena

Uncertainty can be represented in probabilistic terms by transforming PDE-based models to stochastic PDEs (SPDEs). 

See "Uncertainty Quantification Across Length Scales" diagram.

Research Areas: An Integrated Methodology

I.  Mathematical Analysis and Multiscale Formulation of SPDEs

    (Brown-Caltech-Cornell)

• Models of Mathematical Analysis and Multiscale Formation of SPDEs
• Model Reduction via Systematic Multi-Scale Formulation
• Information Theoretic Multiscaling

II.  Numerical Solution of SPDEs

     (Brown-Cornell-Caltech)

• Overview of Numerical Solution of SPDEs
• Concentration of Measure Phenomenon
• Polynomial Chaos - Analysis of Variance (ANOVA)
• Multi-level Monte Carlo Method for SPDEs

III.  Dimension Reduction
      (MIT-Cornell-Brown)

• Reduced-Order Modeling and Synthesis of SPDEs
• Uncertainty Propagation Driven by Data
• Reduced-Order Modeling

IV.  Multiscale Property Estimation

      (Cornell-MIT-Brown)

• Topics of Multiscale Property Estimation

V.  Design and Control Under Uncertainty

     (MIT-Cornell-Brown)

• Objectives and Decision-Making Under Uncertainty
• Heterogeneous Random Materials
• High-Dimensional UQ in Wave Problems

• UQ in Flow-Structure Interactions