An adaptive reduced basis ANOVA method for high-dimensional Bayesian inverse problems

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Colleges, School and Institutes


In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation. However, in many practical problems, the parameter of interest can be of high dimensionality, which renders standard model reduction techniques infeasible. In this paper, we present an approach that employs the ANOVA decomposition method to reduce the model with respect to the unknown parameters, and the reduced basis method to reduce the model with respect to the physical parameters. Moreover, we provide an adaptive scheme within the MCMC iterations, to perform the ANOVA decomposition with respect to the posterior distribution. With numerical examples, we demonstrate that the proposed model reduction method can significantly reduce the computational cost of Bayesian inverse problems, without sacrificing much accuracy.


Original languageEnglish
Pages (from-to)364-380
JournalJournal of Computational Physics
Early online date5 Jul 2019
Publication statusPublished - Nov 2019


  • ANOVA, reduced basis methods, Bayesian inference, Markov Chain Monte Carlo, Inverse problems