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Posterior Covariance Matrix Approximations

Journal Article · · Journal of Verification, Validation and Uncertainty Quantification
DOI:https://doi.org/10.1115/1.4065378· OSTI ID:2406578
 [1];  [2]
  1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Univ. of Colorado, Boulder, CO (United States)
  2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Here, the Davis equation of state (EOS) is commonly used to model thermodynamic relationships for high explosive (HE) reactants. Typically, the parameters in the EOS are calibrated, with uncertainty, using a Bayesian framework and Markov Chain Monte Carlo (MCMC) methods. However, MCMC methods are computationally expensive, especially for complex models with many parameters. This paper provides a comparison between MCMC and less computationally expensive Variational methods (Variational Bayesian and Hessian Variational Bayesian) for computing the posterior distribution and approximating the posterior covariance matrix based on heterogeneous experimental data. All three methods recover similar posterior distributions and posterior covariance matrices. This study demonstrates that for this EOS parameter calibration application, the assumptions made in the two Variational methods significantly reduce the computational cost but do not substantially change the results compared to MCMC.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
Grant/Contract Number:
89233218CNA000001; NA0003962
OSTI ID:
2406578
Report Number(s):
LA-UR--23-31558
Journal Information:
Journal of Verification, Validation and Uncertainty Quantification, Journal Name: Journal of Verification, Validation and Uncertainty Quantification Journal Issue: 1 Vol. 9; ISSN 2377-2158
Publisher:
ASMECopyright Statement
Country of Publication:
United States
Language:
English

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