Comparing frequentist and Bayesian uncertainty quantification in two‐step constitutive model calibration

Abstract

AbstractThe calibration of constitutive models using experimental observations is a well‐established task in computational solid mechanics. Especially for complex constitutive models, multistep calibrations are regularly applied. While this approach is advantageous for reducing the complexity of the calibration problem, the quantification of parameter uncertainties becomes more challenging. In this study, we perform two‐step statistical parameter inference for an elasto‐plastic constitutive model utilizing a frequentist approach and Bayesian inference. The uncertainties are quantified by different methods, in particular, we compare an asymptotic normality analysis and Gaussian error propagation in the frequentist setting with sampling‐based Bayesian inference. Although frequentist and Bayesian parameter inference differ significantly in the way parameters are calibrated, both methods yield similar estimates. Additionally, the uncertainties quantified by asymptotic normality considerations and Gaussian error propagation are quite similar. However, the uncertainties of the elasticity parameters in the frequentist approach are found to be significantly smaller compared to Bayesian inference, due to the underlying approximations in the frequentist setting. Thus, uncertainties can be estimated in both settings, but it is crucial to be aware of the inherent assumptions and simplifications when interpreting the results.