When model-form and parametric uncertainties matter: A unified stochastic representation for propagation and sensitivity analysis

This work develops a new probabilistic framework for uncertainty quantification and sensitivity analysis in computational engineering, focusing on the case of mixed uncertainties arising from both parametric and model-form sources. We introduce a stochastic propagation strategy for multi-model systems where discontinuities and multimodal outputs challenge traditional surrogates. We leverage multi-element polynomial chaos expansions to capture localized behaviors while enabling efficient variance-based sensitivity analysis. We further derive sensitivity indices that measure the relative influence of parametric and model-form uncertainties, offering a principled way to identify which source of uncertainties matters the most in reliability-critical applications. The proposed methodology is exemplified and verified through toy problems and molecular dynamics simulations involving uncertainties in interatomic potentials and external forcing. These contributions provide an integrated approach to propagate, analyze, and compare mixed uncertainties, bridging a critical methodological gap in applications involving multiple model classes and random parameters.

Duke Scholars

Author Johann Guilleminot Thomas Lord Department of Mechanical Engineering and Materia ...