# Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems

arXiv: https://arxiv.org/abs/2212.02250 · HTML: https://mlsanity.com/paper/2212.02250/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 80 references that are in the map.
- First posted on arXiv 5 Dec 2022.

## Builds on (most cited first, 7 of 7)

- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [Polynomial-Chaos-based Kriging](https://mlsanity.com/paper/1502.03939/) (2015)
- [The role of surrogate models in the development of digital twins of dynamic systems](https://mlsanity.com/paper/2001.09292/) (2020)
- [Stochastic spectral embedding](https://mlsanity.com/paper/2004.04480/) (2020)
- [Residual Gaussian Process: A Tractable Nonparametric Bayesian Emulator for Multi-fidelity Simulations](https://mlsanity.com/paper/2104.03743/) (2021)
- [Bayesian model inversion using stochastic spectral embedding](https://mlsanity.com/paper/2005.07380/) (2020)
- [A mechanism-based multi-trap phase field model for hydrogen assisted fracture](https://mlsanity.com/paper/2108.00856/) (2021)

## Built on by (most cited first, 1 of 1)

- [A neural network machine-learning approach for characterising hydrogen trapping parameters from TDS experiments](https://mlsanity.com/paper/2508.03371/) (2025)

## Abstract (arXiv)

This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian inference applications, a multielement Polynomial Chaos Expansion based Kriging metamodel is proposed. The developed surrogate model combines in a piecewise function an array of local Polynomial Chaos based Kriging metamodels constructed on a finite set of non-overlapping subdomains of the stochastic input space. Therewith, the presence of non-smoothness in the response of the forward model (e.g.~ nonlinearities and sparseness) can be reproduced by the proposed metamodel with minimum computational costs owing to its local adaptation capabilities. The model parameter inference is conducted through a Markov chain Monte Carlo approach comprising adaptive exploration and delayed rejection. The efficiency and accuracy of the proposed approach are validated through two case studies, including an analytical benchmark and a numerical case study. The latter relates the partial differential equation governing the hydrogen diffusion phenomenon of metallic materials in Thermal Desorption Spectroscopy tests.