Bayesian probability theory unifies uncertainty quantification in mechanics

Uncertainty quantification (UQ) is critical in mechanics, especially computational mechanics, where two fundamental problem types arise: forward problems (propagating input uncertainties to output quantities of interest) and inverse problems (inferring unknown parameters from experimental observations or simulations). To handle the computational cost of evaluating marginal output distributions, fast data-driven surrogate models are needed. This creates two inverse sub-tasks: identifying and calibrating input uncertainties, and constructing surrogates (surrogate-based UQ). Authors Sascha Ranftl, Malte Rolf, Gerhard A. Holzapfel, and Ellen Kuhl demonstrate that Bayesian probability theory provides a unified theoretical framework for all these tasks.

The framework seamlessly incorporates model selection (choosing the most probable model specifications) and experimental design (optimizing data collection to maximize information gain about parameters). It also connects to sensitivity analysis and the use of special priors like random fields. While the theory is general to all mechanical problems, the paper highlights biomechanics, where inherent biological heterogeneity, patient-specific variability, and noisy data make UQ especially challenging. This work, published on arXiv as 2607.18734, could significantly streamline how engineers and researchers handle uncertainty in simulations and experiments, from structural mechanics to personalized medicine.