Uncertainty quantification in mechanics: A unified Bayesian perspective

2026-07-21

AI Summary

This study addresses the significant uncertainties in biomechanics arising from inter-individual variability and noisy experimental data by proposing a unified framework grounded in Bayesian probability theory. The approach systematically integrates forward uncertainty propagation and inverse parameter inference within a single coherent paradigm. It seamlessly combines input uncertainty characterization, data-driven surrogate modeling, model selection criteria, and information-theoretic optimal experimental design, while naturally linking global sensitivity analysis with spatially correlated random field priors. As the first mechanics-oriented uncertainty quantification methodology to adopt Bayesian inference as a unifying principle, this work delivers a theoretically consistent, computationally efficient, and robust toolkit for both computational and experimental mechanics, substantially enhancing the accuracy of parameter calibration and the reliability of predictive outcomes.

Abstract

Uncertainty quantification (UQ) is essential to experimental mechanics, but has become particularly relevant in computational mechanics, manifesting in two fundamental problem types: forward and inverse problems. The former addresses how input uncertainties propagate to the quantities of interest, whereas the latter aims to infer unknown parameters from experimental observations or simulations. Since efficient propagation typically requires a prohibitive number of evaluations to compute marginal output distributions, the development of fast, data-driven surrogate models becomes necessary. Thus, we can distinguish between two inverse tasks: (i) the identification and calibration of input uncertainties, and (ii) the construction of surrogates, a methodology collectively referred to as surrogate-based UQ. Building on probabilistic reasoning and the concept of partial belief, we demonstrate that Bayesian probability theory provides a unified theoretical framework for addressing both problem types. We further show that Bayesian inference allows for the seamless incorporation of essential subproblems, including model selection for identifying the most probable model specifications and experimental design for optimizing data collection by identifying experiments or simulations that maximize expected information gain about parameters, among others such as connections to sensitivity analysis or the use of special priors like random fields. While this theoretical framework is presented for general mechanical problems, particular emphasis is placed on biomechanics, where variability and uncertainty is especially pronounced due to inherent biological heterogeneity, patient-specific variability, and noisy data.

Problem

• uncertainty quantification
• forward problem
• inverse problem
• biomechanics
• Bayesian inference

Innovation

• Bayesian inference
• uncertainty quantification
• surrogate modeling
• experimental design
• biomechanics