The Use of Radial Basis Function Surrogate Models for Sampling Process Acceleration in Bayesian Inversion

The Bayesian approach provides a natural way of solving engineering inverse problems including uncertainties. The objective is to describe unknown parameters of a mathematical model based on noisy measurements. Using the Bayesian approach, the vector of unknown parameters is described by its joint probability distribution, i.e. the posterior distribution. To provide samples, Markov Chain Monte Carlo methods can be used. Their disadvantage lies in the need of repeated evaluations of the mathematical model that are computationally expensive in the case of practical problems.

[1]  Jari P. Kaipio,et al.  The Bayesian Framework for Inverse Problems in Heat Transfer , 2011 .

[2]  Ming Ye,et al.  An adaptive sparse‐grid high‐order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling , 2013 .

[3]  T. J. Dodwell,et al.  A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow , 2013, SIAM/ASA J. Uncertain. Quantification.

[4]  Andrew M. Stuart,et al.  Inverse problems: A Bayesian perspective , 2010, Acta Numerica.

[5]  Christian P. Robert,et al.  The Bayesian choice : from decision-theoretic foundations to computational implementation , 2007 .

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

[7]  Martin D. Buhmann,et al.  Radial Basis Functions: Theory and Implementations: Preface , 2003 .

[8]  Jie Liu,et al.  A fast Bayesian approach using adaptive densifying approximation technique accelerated MCMC , 2016 .

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

[10]  Binayak P. Mohanty,et al.  Efficient uncertainty quantification techniques in inverse problems for Richards’ equation using coarse-scale simulation models , 2009 .

[11]  Tiangang Cui,et al.  Bayesian calibration of a large‐scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm , 2011 .

[12]  Daniil Svyatskiy,et al.  Multilevel approximations in sample-based inversion from the Dirichlet-to-Neumann map , 2008 .

[13]  Andrew Golightly,et al.  Adaptive, Delayed-Acceptance MCMC for Targets With Expensive Likelihoods , 2015, 1509.00172.

[14]  Tiangang Cui,et al.  Data‐driven model reduction for the Bayesian solution of inverse problems , 2014, 1403.4290.

[15]  Simona Domesová,et al.  A Bayesian Approach to the Identification Problem with Given Material Interfaces in the Darcy Flow , 2017, HPCSE.