Dimension reduction for efficient Bayesian inference of high-dimensional quantity of interest problems with parametric and nonparametric uncertainties

Abstract

This paper addresses the challenges of efficient Bayesian inverse analysis for high-dimensional parameter spaces and quantities of interest (QoIs), such as output fields. Two main challenges are identified: (i) the need for numerous forward model evaluations during posterior sampling, and (ii) the exploration of the high-dimensional parameter space. To address the first challenge, a probabilistic surrogate model based on polynomial chaos expansions (PCE) is proposed. However, PCE for high-dimensional parameter spaces faces difficulties in robust uncertainty quantification. Although basis adaptation in PCE is promising for low-dimensional QoIs, it struggles with high-dimensional output fields and convergence issues. Additionally, modeling errors introduce further uncertainties.

To overcome these challenges, an integrated approach employing dimension reduction techniques for both the QoI and parameter space is introduced. For the QoI, a truncated Karhunen-Loève expansion (KLE) is used, and for the parameter space, basis adaptation with convergence acceleration algorithms is applied. This results in a surrogate model that replaces the physical model, significantly improving computational efficiency. To account for uncertainties due to modeling errors, a nonparametric stochastic approach is incorporated into the surrogate model. For the second challenge in Bayesian inference, a block-update Markov Chain Monte Carlo (MCMC) algorithm is applied to promote mixingand enhance the acceptance rate of posterior sampling. The effectiveness of the methods is validated through detailed cases of boiling water reactor spent nuclear fuel assemblies and fully-loaded spent nuclear fuel canisters, demonstrating the applicability and efficiency of the integrated surrogate modeling and block-update MCMC for high-dimensional problems.