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PARAMETER AND STATE MODEL REDUCTION FOR LARGE-SCALE STATISTICAL INVERSE PROBLEMS CHAD LIEBERMAN∗ , KAREN WILLCOX† , AND OMAR GHATTAS‡ Abstract. A greedy algorithm for the construction of a reduced model with reduct

Source URL: raphael.mit.edu

• Markov models
• Monte Carlo methods
• Statistical theory
• Markov chain Monte Carlo
• Inverse problem
• Parameter space
• Markov chain
• Estimation theory
• Bayesian inference
• Statistics
• Statistical inference
• Bayesian statistics

AIAA JOURNAL Vol. 46, No. 10, October 2008 Parametric Reduced-Order Models for Probabilistic Analysis of Unsteady Aerodynamic Applications T. Bui-Thanh∗ and K. Willcox†

Source URL: raphael.mit.edu

• Regression analysis
• Data analysis
• Computational fluid dynamics
• Navier–Stokes equations
• Least squares
• Principal component analysis
• Parameter space
• Combinatorics
• Combinatory logic
• Statistics
• Mathematics
• Mathematical optimization

MIT Aerospace Computational Design Laboratory Technical Report TR-13-1, June[removed]LOCALIZED DISCRETE EMPIRICAL INTERPOLATION METHOD BENJAMIN PEHERSTORFER∗ , DANIEL BUTNARU∗ , KAREN WILLCOX† , AND HANS-JOACHIM BUN

Source URL: raphael.mit.edu

• Numerical analysis
• Multivariate statistics
• Multivariable calculus
• Partial differential equation
• Principal component analysis
• Mathematical optimization
• Interpolation
• Galerkin method
• Differential equation
• Mathematics
• Mathematical analysis
• Statistics

AIAA[removed]BALANCED MODEL REDUCTION VIA THE PROPER ORTHOGONAL DECOMPOSITION K. Willcox and J. Peraire Fluid Dynamics Research Laboratory

Source URL: raphael.mit.edu

• Control theory
• Hankel singular value
• State space
• Principal component analysis
• Eigenvalues and eigenvectors
• Controllability
• Observability
• Lanczos algorithm
• Gramian matrix
• Algebra
• Linear algebra
• Mathematics

A DOMAIN DECOMPOSITION APPROACH FOR UNCERTAINTY ANALYSIS QIFENG LIAO∗ AND KAREN WILLCOX† Abstract. This paper proposes a decomposition approach for uncertainty analysis of systems governed by partial differential equ

Source URL: web.mit.edu

• Multivariable calculus
• Partial differential equation
• Xi
• Continuous function
• Sinc function
• Mathematical analysis
• Mathematics
• Domain decomposition methods

MODEL REDUCTION FOR LARGE-SCALE SYSTEMS WITH HIGH-DIMENSIONAL PARAMETRIC INPUT SPACE T. BUI-THANH∗ , K. WILLCOX† , AND O. GHATTAS‡ Abstract. A model-constrained adaptive sampling methodology is proposed for reducti

Source URL: raphael.mit.edu

• Operations research
• Least squares
• Degrees of freedom
• Statistical inference
• Statistics
• Regression analysis
• Mathematical optimization

AIAA JOURNAL Vol. 48, No. 8, August 2010 Surrogate Modeling for Uncertainty Assessment with Application to Aviation Environmental System Models D. Allaire∗ and K. Willcox†

Source URL: raphael.mit.edu

• Data analysis
• Process management
• Scientific modeling
• Sensitivity analysis
• Variance
• Normal distribution
• Estimation theory
• Surrogate model
• Propagation of uncertainty
• Statistics
• Numerical analysis
• Design of experiments

Unsteady Flow Sensing and Estimation via the Gappy Proper Orthogonal Decomposition K. Willcox∗ Aerospace Computational Design Laboratory Massachusetts Institute of Technology January 26, 2004

Source URL: web.mit.edu

• Abstract algebra
• Vector space
• Principal component analysis
• Navier–Stokes equations
• Euclidean vector
• Flow measurement
• Eigenvalues and eigenvectors
• Basis
• Orthogonality
• Algebra
• Mathematics
• Linear algebra

Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems M. Frangos, Y. Marzouk, K. Willcox, Massachusetts Institute of Technology; B. van Bloemen Waanders,

Source URL: raphael.mit.edu

• Econometrics
• Measurement
• Statistical inference
• Statistical theory
• Inverse problem
• Monte Carlo method
• Dimensional analysis
• Markov chain Monte Carlo
• Estimator
• Statistics
• Probability and statistics
• Estimation theory