Data‐driven model reduction for the Bayesian solution of inverse problems
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[1] Jun S. Liu,et al. Monte Carlo strategies in scientific computing , 2001 .
[2] Andrew M. Stuart,et al. Inverse problems: A Bayesian perspective , 2010, Acta Numerica.
[3] Karen Willcox,et al. Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems , 2010, SIAM J. Sci. Comput..
[4] M. J. Bayarri,et al. Predicting Vehicle Crashworthiness: Validation of Computer Models for Functional and Hierarchical Data , 2009 .
[5] Stefan Volkwein,et al. Proper orthogonal decomposition for optimality systems , 2008 .
[6] N. Nguyen,et al. An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations , 2004 .
[7] C. Fox,et al. Markov chain Monte Carlo Using an Approximation , 2005 .
[8] L. Sirovich. TURBULENCE AND THE DYNAMICS OF COHERENT STRUCTURES PART I : COHERENT STRUCTURES , 2016 .
[9] James Martin,et al. A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion , 2012, SIAM J. Sci. Comput..
[10] David Galbally,et al. Non‐linear model reduction for uncertainty quantification in large‐scale inverse problems , 2009 .
[11] Marcus Meyer,et al. Efficient model reduction in non-linear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods , 2003 .
[12] S. S. Ravindran,et al. Adaptive Reduced-Order Controllers for a Thermal Flow System Using Proper Orthogonal Decomposition , 2001, SIAM J. Sci. Comput..
[13] E. Somersalo,et al. Statistical and computational inverse problems , 2004 .
[14] H. Haario,et al. An adaptive Metropolis algorithm , 2001 .
[15] Charbel Farhat,et al. Nonlinear model order reduction based on local reduced‐order bases , 2012 .
[16] J. Hesthaven,et al. Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations , 2007 .
[17] E. Sachs,et al. Trust-region proper orthogonal decomposition for flow control , 2000 .
[18] Maurizio Dapor. Monte Carlo Strategies , 2020, Transport of Energetic Electrons in Solids.
[19] L. Sirovich. Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .
[20] Michael I. Miller,et al. REPRESENTATIONS OF KNOWLEDGE IN COMPLEX SYSTEMS , 1994 .
[21] N. Metropolis,et al. Equation of State Calculations by Fast Computing Machines , 1953, Resonance.
[22] M. Girolami,et al. Riemann manifold Langevin and Hamiltonian Monte Carlo methods , 2011, Journal of the Royal Statistical Society: Series B (Statistical Methodology).
[23] H. Haario,et al. Markov chain Monte Carlo methods for high dimensional inversion in remote sensing , 2004 .
[24] Benjamin Peherstorfer,et al. Localized Discrete Empirical Interpolation Method , 2014, SIAM J. Sci. Comput..
[25] Habib N. Najm,et al. Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems , 2008, J. Comput. Phys..
[26] Jari P. Kaipio,et al. Electrical impedance tomography imaging with reduced-order model based on proper orthogonal decomposition , 2013, J. Electronic Imaging.
[27] James O. Berger,et al. Markov chain Monte Carlo-based approaches for inference in computationally intensive inverse problems , 2003 .
[28] J. Rosenthal,et al. Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms , 2007, Journal of Applied Probability.
[29] Benjamin Stamm,et al. Parameter multi‐domain ‘hp’ empirical interpolation , 2012 .
[30] Habib N. Najm,et al. Stochastic spectral methods for efficient Bayesian solution of inverse problems , 2005, J. Comput. Phys..
[31] Karen Willcox,et al. Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space , 2008, SIAM J. Sci. Comput..
[32] Danny C. Sorensen,et al. Nonlinear Model Reduction via Discrete Empirical Interpolation , 2010, SIAM J. Sci. Comput..
[33] Jun S. Liu,et al. Sequential Monte Carlo methods for dynamic systems , 1997 .
[34] Geoff K. Nicholls,et al. Statistical inversion of South Atlantic circulation in an abyssal neutral density layer , 2005 .
[35] Charbel Farhat,et al. A Compact Proper Orthogonal Decomposition Basis for Optimization-Oriented Reduced-Order Models , 2008 .
[36] W. K. Hastings,et al. Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .
[37] Siep Weiland,et al. Missing Point Estimation in Models Described by Proper Orthogonal Decomposition , 2004, IEEE Transactions on Automatic Control.
[38] Bernard Haasdonk,et al. A training set and multiple bases generation approach for parameterized model reduction based on adaptive grids in parameter space , 2011 .
[39] Albert Tarantola,et al. Inverse problem theory - and methods for model parameter estimation , 2004 .
[40] Thomas M. Cover,et al. Elements of Information Theory , 2005 .
[41] Tiangang Cui,et al. Bayesian calibration of geothermal reservoir models via Markov Chain Monte Carlo , 2010 .
[42] Nicholas Zabaras,et al. Using Bayesian statistics in the estimation of heat source in radiation , 2005 .
[43] Tiangang Cui,et al. Bayesian calibration of a large‐scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm , 2011 .