Multi-model polynomial chaos surrogate dictionary for Bayesian inference in elasticity problems

[1]  W. Aquino,et al.  Stochastic reduced order models for inverse problems under uncertainty. , 2015, Computer methods in applied mechanics and engineering.

[2]  O. Knio,et al.  Drag Parameter Estimation Using Gradients and Hessian from a Polynomial Chaos Model Surrogate , 2014 .

[3]  Marco A. Iglesias,et al.  Well-posed Bayesian geometric inverse problems arising in subsurface flow , 2014, 1401.5571.

[4]  Akhtar A. Khan,et al.  An equation error approach for the elasticity imaging inverse problem for predicting tumor location , 2014, Comput. Math. Appl..

[5]  Omar Ghattas,et al.  Site characterization using full waveform inversion , 2013 .

[6]  Marc Bonnet,et al.  Large Scale Parameter Estimation Problems in Frequency-Domain Elastodynamics Using an Error in Constitutive Equation Functional. , 2013, Computer methods in applied mechanics and engineering.

[7]  Michael McVay,et al.  Site characterization using Gauss–Newton inversion of 2-D full seismic waveform in the time domain , 2012 .

[8]  P. S. Koutsourelakis,et al.  A novel Bayesian strategy for the identification of spatially varying material properties and model validation: an application to static elastography , 2012, 1512.05913.

[9]  Omar M. Knio,et al.  Global sensitivity analysis in an ocean general circulation model: a sparse spectral projection approach , 2012, Computational Geosciences.

[10]  B. D. Reddy,et al.  Introduction to finite element analysis and recent developments , 2012 .

[11]  Zhishen Wu,et al.  Vibration‐Based Damage Localization in Flexural Structures Using Normalized Modal Macrostrain Techniques from Limited Measurements , 2011, Comput. Aided Civ. Infrastructure Eng..

[12]  Franck Schoefs,et al.  Polynomial Chaos Representation for Identification of Mechanical Characteristics of Instrumented Structures , 2011, Comput. Aided Civ. Infrastructure Eng..

[13]  Sami F. Masri,et al.  Finite Element Model Updating Using Evolutionary Strategy for Damage Detection , 2011, Comput. Aided Civ. Infrastructure Eng..

[14]  Dirk P. Kroese,et al.  Kernel density estimation via diffusion , 2010, 1011.2602.

[15]  O. L. Maître,et al.  Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics , 2010 .

[16]  Mostafa Fatemi,et al.  An Inverse Problem Approach for Elasticity Imaging through Vibroacoustics , 2010, IEEE Transactions on Medical Imaging.

[17]  Haim Azhari,et al.  A Method for Characterization of Tissue Elastic Properties Combining Ultrasonic Computed Tomography With Elastography , 2010, Journal of ultrasound in medicine : official journal of the American Institute of Ultrasound in Medicine.

[18]  Omar M. Knio,et al.  Spectral Methods for Uncertainty Quantification , 2010 .

[19]  Y. Marzouk,et al.  A stochastic collocation approach to Bayesian inference in inverse problems , 2009 .

[20]  Nicholas Zabaras,et al.  An efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method , 2009 .

[21]  Bangti Jin,et al.  Fast Bayesian approach for parameter estimation , 2008 .

[22]  Fabio Nobile,et al.  A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data , 2008, SIAM J. Numer. Anal..

[23]  Baskar Ganapathysubramanian,et al.  A scalable framework for the solution of stochastic inverse problems using a sparse grid collocation approach , 2008, J. Comput. Phys..

[24]  Bangti Jin,et al.  Inversion of Robin coefficient by a spectral stochastic finite element approach , 2008, J. Comput. Phys..

[25]  Habib N. Najm,et al.  Stochastic spectral methods for efficient Bayesian solution of inverse problems , 2005, J. Comput. Phys..

[26]  Fabio Nobile,et al.  A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data , 2007, SIAM Rev..

[27]  M. Fink,et al.  Nonlinear viscoelastic properties of tissue assessed by ultrasound , 2006, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[28]  Roger Ghanem,et al.  Stochastic inversion in acoustic scattering , 2006 .

[29]  Yalchin Efendiev,et al.  Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models , 2006, SIAM J. Sci. Comput..

[30]  C. Fox,et al.  Markov chain Monte Carlo Using an Approximation , 2005 .

[31]  Yalchin Efendiev,et al.  An efficient two‐stage Markov chain Monte Carlo method for dynamic data integration , 2005 .

[32]  R. B. Jackson,et al.  Hydrological consequences of Eucalyptus afforestation in the Argentine Pampas , 2005 .

[33]  Nicholas Zabaras,et al.  Using Bayesian statistics in the estimation of heat source in radiation , 2005 .

[34]  Elisa E Konofagou,et al.  Estimation of material elastic moduli in elastography: a local method, and an investigation of Poisson's ratio sensitivity. , 2004, Journal of biomechanics.

[35]  N. Zabaras,et al.  Stochastic inverse heat conduction using a spectral approach , 2004 .

[36]  J Bercoff,et al.  Monitoring Thermally-Induced Lesions with Supersonic Shear Imaging , 2004, Ultrasonic imaging.

[37]  Panos G. Georgopoulos,et al.  Uncertainty reduction and characterization for complex environmental fate and transport models: An empirical Bayesian framework incorporating the stochastic response surface method , 2003 .

[38]  J. Greenleaf,et al.  Selected methods for imaging elastic properties of biological tissues. , 2003, Annual review of biomedical engineering.

[39]  Diane M. McKnight,et al.  Transport and cycling of iron and hydrogen peroxide in a freshwater stream: Influence of organic acids , 2003 .

[40]  Habib N. Najm,et al.  A multigrid solver for two-dimensional stochastic diffusion equations , 2003 .

[41]  Assad A. Oberai,et al.  INVERSE PROBLEMS PII: S0266-5611(03)54272-1 Solution of inverse problems in elasticity imaging using the adjoint method , 2003 .

[42]  James O. Berger,et al.  Markov chain Monte Carlo-based approaches for inference in computationally intensive inverse problems , 2003 .

[43]  M. Fink,et al.  Shear elasticity probe for soft tissues with 1-D transient elastography , 2002, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[44]  A. Mohammad-Djafari Bayesian inference for inverse problems , 2001, physics/0110093.

[45]  Luis Tenorio,et al.  Statistical Regularization of Inverse Problems , 2001, SIAM Rev..

[46]  Aleksey V. Nenarokomov,et al.  Uncertainties in parameter estimation: the optimal experiment design , 2000 .

[47]  R. Ghanem,et al.  Iterative solution of systems of linear equations arising in the context of stochastic finite elements , 2000 .

[48]  J. Bishop,et al.  Visualization and quantification of breast cancer biomechanical properties with magnetic resonance elastography. , 2000, Physics in medicine and biology.

[49]  J F Greenleaf,et al.  Vibro-acoustography: an imaging modality based on ultrasound-stimulated acoustic emission. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[50]  A. Mohammad-Djafari A full Bayesian approach for inverse problems , 2001, physics/0111123.

[51]  W. O’Brien,et al.  Young's modulus measurements of soft tissues with application to elasticity imaging , 1996, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[52]  Jonathan Richard Shewchuk,et al.  Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator , 1996, WACG.

[53]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[54]  C. Sumi,et al.  Estimation of shear modulus distribution in soft tissue from strain distribution , 1995, IEEE Transactions on Biomedical Engineering.

[55]  L. Tierney Markov Chains for Exploring Posterior Distributions , 1994 .

[56]  K. R. Raghavan,et al.  Forward and inverse problems in elasticity imaging of soft tissues , 1994 .

[57]  Ali Mohammad-Djafari,et al.  On the estimation of hyperparameters in Bayesian approach of solving inverse problems , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[58]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[59]  K J Parker,et al.  Tissue response to mechanical vibrations for "sonoelasticity imaging". , 1990, Ultrasound in medicine & biology.

[60]  J. Achenbach THE LINEARIZED THEORY OF ELASTICITY , 1973 .