A differentiable PCA-GPR surrogate framework for full-transient Bayesian inverse uncertainty quantification of black-box nuclear thermal-hydraulic systems
Abstract
Complex transient energy systems require uncertainty-quantified predictions, but Bayesian inverse uncertainty quantification (IUQ) is often impractical because posterior sampling with high-fidelity system codes requires many expensive full-transient simulations. This study develops a surrogate-assisted Bayesian IUQ framework that makes full-time-series calibration practical for the NACIE heavy-liquid-metal natural-circulation loop. The key innovation is to transform a black-box transient simulator into a differentiable probabilistic emulator by combining principal component analysis with Gaussian process regression (PCA--GPR). The surrogate reconstructs complete multichannel temperature and mass-flow histories from a compact latent representation, preserving dominant temporal and cross-channel correlations while enabling automatic differentiation of the log posterior. This allows both gradient-free ensemble slice sampling and gradient-informed sampling with the No-U-Turn Sampler and Microcanonical Langevin Monte Carlo. Five principal components capture more than 99\% of the output variance, and the surrogate achieves normalized root-mean-square errors below 2\%. Compared with direct Flownex SE evaluations, the surrogate reduces likelihood-evaluation cost by approximately 3000-fold while preserving posterior statistics and correlations. Posterior predictive analyses show reduced bias, narrower intervals, and improved agreement with measurements and independent validation.
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BibTeX
@misc{yaoa2026differentiable,
title = {{A differentiable PCA-GPR surrogate framework for full-transient Bayesian inverse uncertainty quantification of black-box nuclear thermal-hydraulic systems}},
author = {Zikang Yaoa and Eugene Yeea and Fue-Sang Lien},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20978},
eprint = {2610.20978},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20978},
}
RIS
TY - UNPB
TI - A differentiable PCA-GPR surrogate framework for full-transient Bayesian inverse uncertainty quantification of black-box nuclear thermal-hydraulic systems
AU - Zikang Yaoa
AU - Eugene Yeea
AU - Fue-Sang Lien
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20978
UR - https://arxiv.org/abs/2610.20978
AB - Complex transient energy systems require uncertainty-quantified predictions, but Bayesian inverse uncertainty quantification (IUQ) is often impractical because posterior sampling with high-fidelity system codes requires many expensive full-transient simulations. This study develops a surrogate-assisted Bayesian IUQ framework that makes full-time-series calibration practical for the NACIE heavy-liquid-metal natural-circulation loop. The key innovation is to transform a black-box transient simulator into a differentiable probabilistic emulator by combining principal component analysis with Gaussian process regression (PCA--GPR). The surrogate reconstructs complete multichannel temperature and mass-flow histories from a compact latent representation, preserving dominant temporal and cross-channel correlations while enabling automatic differentiation of the log posterior. This allows both gradient-free ensemble slice sampling and gradient-informed sampling with the No-U-Turn Sampler and Microcanonical Langevin Monte Carlo. Five principal components capture more than 99\% of the output variance, and the surrogate achieves normalized root-mean-square errors below 2\%. Compared with direct Flownex SE evaluations, the surrogate reduces likelihood-evaluation cost by approximately 3000-fold while preserving posterior statistics and correlations. Posterior predictive analyses show reduced bias, narrower intervals, and improved agreement with measurements and independent validation.
ER -