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Hierarchical structured Stochastic Variational Inference for uncertainty quantification of viscoplastic constitutive models.

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Title: Hierarchical structured Stochastic Variational Inference for uncertainty quantification of viscoplastic constitutive models.
Authors: Chen, Tianju1,2 (AUTHOR) chentianju@usst.edu.cn, Messner, Mark C.1,2 (AUTHOR) messner@anl.gov, Fu, Huadong1,3 (AUTHOR) hdfu@ustb.edu.cn
Source: European Journal of Mechanics A: Solids. Sep2026, Vol. 119, pN.PAG-N.PAG. 1p.
Subjects: Hierarchical Bayes model, Bayesian analysis, Uncertainty (Information theory), Mechanical behavior of materials, Calibration
Abstract: We present a Bayesian approach to constitutive modeling that leverages Stochastic Variational Inference (SVI) for efficient uncertainty quantification of viscoplastic material response. Traditional methods struggle to characterize variability from material heterogeneity and experimental noise with limited datasets. Our SVI implementation in pyoptmat overcomes this by: (1) Using hierarchical priors to share statistical strength across temperatures, reducing data requirements compared to non-hierarchical methods; (2) Enabling rapid posterior estimation (much faster than Markov Chain Monte Carlo (MCMC)) through stochastic gradient optimization; and (3) Preserving full uncertainty quantification via variational distributions. Validated against synthetic data and applied to Alloy 800H at multiple temperatures, the approach produces temperature-dependent statistical models that accurately capture stress–strain uncertainty. The hierarchical SVI framework is especially adept at handling sparse experimental data, effectively distinguishing between true material variability and experimental noise where traditional calibration techniques cannot. Our approach bypasses the computational limitations that have traditionally hindered full uncertainty propagation in complex constitutive models. This capability leads to substantially improved model calibration and robust extrapolation, enhancing the model's utility in engineering design and analysis. • Hierarchical priors share info across temps, reducing data needs vs standard methods • SVI is much faster than MCMC, enabling rapid model calibration • pyoptmat gives full UQ via var. distributions, typically hard for complex models • Validated on synthetic & real data for Alloy 800H, giving accurate T-dependent models • Leads to better calibration & robust extrapolation, improving design & safety utility [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:We present a Bayesian approach to constitutive modeling that leverages Stochastic Variational Inference (SVI) for efficient uncertainty quantification of viscoplastic material response. Traditional methods struggle to characterize variability from material heterogeneity and experimental noise with limited datasets. Our SVI implementation in pyoptmat overcomes this by: (1) Using hierarchical priors to share statistical strength across temperatures, reducing data requirements compared to non-hierarchical methods; (2) Enabling rapid posterior estimation (much faster than Markov Chain Monte Carlo (MCMC)) through stochastic gradient optimization; and (3) Preserving full uncertainty quantification via variational distributions. Validated against synthetic data and applied to Alloy 800H at multiple temperatures, the approach produces temperature-dependent statistical models that accurately capture stress–strain uncertainty. The hierarchical SVI framework is especially adept at handling sparse experimental data, effectively distinguishing between true material variability and experimental noise where traditional calibration techniques cannot. Our approach bypasses the computational limitations that have traditionally hindered full uncertainty propagation in complex constitutive models. This capability leads to substantially improved model calibration and robust extrapolation, enhancing the model's utility in engineering design and analysis. • Hierarchical priors share info across temps, reducing data needs vs standard methods • SVI is much faster than MCMC, enabling rapid model calibration • pyoptmat gives full UQ via var. distributions, typically hard for complex models • Validated on synthetic & real data for Alloy 800H, giving accurate T-dependent models • Leads to better calibration & robust extrapolation, improving design & safety utility [ABSTRACT FROM AUTHOR]
ISSN:09977538
DOI:10.1016/j.euromechsol.2026.106139