Comparison of random field discretizations for high-resolution Bayesian parameter identification in finite element elasticity

TL;DR

This paper compares three random field discretization methods for Bayesian parameter identification in finite element elasticity, focusing on efficiency and accuracy at high resolutions.

Contribution

It provides a comparative analysis of Karhunen-Loève, wavelet, and local subdivision methods for stochastic modeling in high-resolution finite element problems.

Findings

All methods produce similar posterior estimates.

Local subdivision improves mixing and reduces cost-to-error at high resolutions.

Differences in variance reduction and sampling efficiency are significant among methods.

Abstract

We compare three random field discretization strategies for probabilistic identification of spatially varying material parameters in high-resolution finite element models. These strategies are (i) the Karhunen-Lo\`eve expansion, (ii) a wavelet expansion, and (iii) local average subdivision. The methods are assessed in the context of multilevel Markov chain Monte Carlo applied to plane stress elasticity with high-resolution displacement observations. Emphasis is placed on numerical efficiency, initialization cost, Markov chain mixing, and cost-to-error behaviour as the discretization resolution increases. While all approaches yield comparable posterior estimates, significant differences are observed in multilevel variance reduction and sampling efficiency. In particular, local average subdivision exhibits improved mixing and lower cost-to-error ratios at fine resolutions, despite its higher nominal parameter dimension. The results provide practical guidance for selecting stochastic field representations in uncertainty quantification in finite element simulations of heterogeneous materials.