Stochastic spectral methods for efficient Bayesian solution of inverse problems

By Youssef M. Marzouk, Habib N. Najm, Larry A. Rahn. Journal of Computational Physics, 2005

516 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Civil and Structural Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5405f84a66fc8c0a13f9c979eea0ba2a256e19e6

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Citations in the corpus

A stochastic collocation approach to Bayesian inference in inverse problems (2009, methodology): “Recent work [17] used (generalized) polynomial chaos (gPC)-based stochastic Galerkin methods [8, 29] to propagate prior uncertainty through the forward model, thus yielding a polynomial approximation of the forward solution over the support of the prior.”
Fast Numerical Methods for Stochastic Computations: A Review (2009, background): “1), and the examples are for linear problems, the gPC framework can be readily applied to complex problems including the time-dependent and nonlinear ones, for example, Burgers’ equation [34, 94], fluid dynamics [40, 41, 44, 46, 92], flow-structure interactions [96], hyperbolic problems [11,31], mat”
Simulation-based optimal Bayesian experimental design for nonlinear systems (2011, methodology): “, [56, 57, 58]), and this is the approach we shall use.”
Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations (2013, methodology): “In [33] and [48], the polynomial chaos expansion has been applied to accelerate Bayesian updating via Markov chain Monte Carlo (MCMC)”
Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces (2013, unknown): “This strategy has had great success in forward [19, 26] and inverse uncertainty propagation problems [29, 4, 12] as well as optimization [24, 39].”
Characterization of reservoir simulation models using a polynomial chaos‐based ensemble Kalman filter (2009, methodology): “Efforts along similar lines have already been reported whereby polynomial chaos representations have been used to accelerate the convergence of Markov chain Monte Carlo methods used in Bayesian estimation [Marzouk et al., 2007].”
Dynamically orthogonal field equations for continuous stochastic dynamical systems (2009, background): “Research is underway for developing DO schemes for data assimilation [69–71] or Bayesian inference [72] in idealized and realistic dynamical systems.”
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems (2008, methodology): “In the inverse context, the Bayesian formulation in [6] constructs a stochastic forward problem whose random inputs span the support of the prior and seeks its solution using Galerkin methods.”
Bayesian Solution Uncertainty Quantification for Differential Equations (2013, background): “…and in particular those based on mathematical descriptions of complex phenomena such as the weather, ocean currents, ice sheet ﬂow, and cellular protein transport (Ghanem and Spanos, 2003; Kaipio et al., 2004; Huttunen and Kaipio, 2007; Marzouk et al., 2007; Marzouk and Najm, 2009; Stuart, 2010).”
Stochastic Collocation Algorithms Using l1-Minimization for Bayesian Solution of Inverse Problems (2015, methodology): “2) is called the stochastic surrogate model [25, 26, 27, 28].”
A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion (2012, methodology): “This stochastic problem is more expensive than the original forward problem, but once obtained, the solution can be used to construct a surrogate for the posterior distribution, which can be evaluated repeatedly at negligible cost, making it ideal for MCMC sampling [30, 32].”