# Uncertainty quantification in mechanics: A unified Bayesian perspective

arXiv: https://arxiv.org/abs/2607.18734 · HTML: https://mlsanity.com/paper/2607.18734/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 265 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 21 of 21)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
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- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [CatBoost: unbiased boosting with categorical features](https://mlsanity.com/paper/1706.09516/) (2017)
- [BoTorch: A Framework for Efficient Monte-Carlo Bayesian Optimization](https://mlsanity.com/paper/1910.06403/) (2019)
- [A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurements](https://mlsanity.com/paper/2204.00205/) (2022)
- [PCE-PINNs: Physics-Informed Neural Networks for Uncertainty Propagation in Ocean Modeling](https://mlsanity.com/paper/2105.02939/) (2021)
- [Bayesian optimal experimental design with Wasserstein information criteria](https://mlsanity.com/paper/2504.10092/) (2025)
- [Separable Operator Networks](https://mlsanity.com/paper/2407.11253/) (2024)
- [Deep Polynomial Chaos Expansion](https://mlsanity.com/paper/2507.21273/) (2025)
- [Compromise-free Bayesian neural networks](https://mlsanity.com/paper/2004.12211/) (2020)
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- [On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiological boundary conditions](https://mlsanity.com/paper/2506.11683/) (2025)
- [Multimodal Neural Operators for Real-Time Biomechanical Modelling of Traumatic Brain Injury](https://mlsanity.com/paper/2510.03248/) (2025)
- [Bayesian Model Selection for Complex Flows of Yield Stress Fluids](https://mlsanity.com/paper/2601.10115/) (2026)
- [An Efficient Bayesian Framework for Inverse Problems via Optimization and Inversion: Surrogate Modeling, Parameter Inference, and Uncertainty Quantification](https://mlsanity.com/paper/2602.04537/) (2026)
- [FalconBC: Flow matching for Amortized inference of Latent-CONditioned physiologic Boundary Conditions](https://mlsanity.com/paper/2603.19331/) (2026)
- [Scalable High-Dimensional Bayesian Field Reconstruction with Finite Elements: Application to 3D Porous Media Flow](https://mlsanity.com/paper/2605.24682/) (2026)

## Abstract (arXiv)

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.