Hierarchical Bayesian models for inverse problems in heat conduction

By Jingbo Wang, Nicholas Zabaras. 2005

173 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b7177482860a826f917e31d143f100c2ddb817cb

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Citations in the corpus

Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real‐Time Bayesian Parameter Estimation (2010, methodology): “We apply the Bayesian approach to parameter estimation Mosegaard and Tarantola (2002); Wang and Zabaras (2005a) to the FE “truth” discretization of the forward problem (1).”
A unified framework for multilevel uncertainty quantification in Bayesian inverse problems (2016, unknown): “Classical inverse problems are sometimes phrased within a hierarchical frame [7, 8].”
A stochastic collocation approach to Bayesian inference in inverse problems (2009, background): “The Bayesian approach to inverse problems [6,13,18,22,23] provides a foundation for inference from noisy and incomplete data, a natural mechanism for incorporating physical constraints and heterogeneous sources of information, and a quantitative assessment of uncertainty in the inverse solution.”
A survey of applications of the MFS to inverse problems (2011, background): “been some recent interest in using statistical Bayesian inference for solving inverse problems [38,39].”
A markov random field model of contamination source identification in porous media flow (2006, methodology): “In [11], the canonical MRF model was enhanced to model random fields with different temporal and spatial length scales and to resolve discontinuities in the unknown fields.”
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems (2008, methodology): “Bayesian approaches to inverse problems have received much recent interest [4, 48, 49], with applications ranging from geophysics [50, 51] and climate modeling [52] to heat transfer [20, 53].”
On Iterative Learning Control of parabolic distributed parameter systems (2009, background): “Applications include heat transfer [15] and option pricing of financial derivatives [16].”
Stochastic spectral methods for efficient Bayesian solution of inverse problems (2005, background): “Bayesian approaches to inverse problems have seen much recent interest [3,5,2], with applications ranging from geophysics [6,7] and climate modeling [8] to heat transfer [9,10].”