Uncertainty quantification in mechanics: A unified Bayesian perspective

• URL: http://arxiv.org/abs/2607.18734v1
• Date: Tue, 21 Jul 2026 05:46:28 GMT
• Title: Uncertainty quantification in mechanics: A unified Bayesian perspective
• Abstract summary: Uncertainty quantification (UQ) is essential to experimental mechanics, but has become particularly relevant in computational mechanics.<n>We show that Bayesian probability theory provides a unified theoretical framework for addressing both problem types.<n>While this theoretical framework is presented for general mechanical problems, particular emphasis is placed on biomechanics, where variability and uncertainty is especially pronounced.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Neural network surrogates with uncertainty quantification for inverse problems in partial differential equations [11.776563892451817]
  We introduce DeepGaLA, a neural-network surrogate for differential equation solvers that provides uncertainty-aware predictions.<n>Across a range of numerical experiments, DeepGaLA delivers forward-model approximations with accuracy comparable to established Gaussian-process surrogates.
  arXiv  Detail & Related papers  (2026-06-18T16:02:20Z)
• Computational Identifiability [58.12019389497595]
  'Identical identifiability' assumes properties, infinite data, or other mathematically idealized conditions.<n>'Computational identifiability' is to instead define a finite computational search procedure for an empirical estimator.<n>We show how this framework allows us to answer fine-grained, practical identification questions.
  arXiv  Detail & Related papers  (2026-06-08T19:39:59Z)
• Contrastive Normalizing Flows for Uncertainty-Aware Parameter Estimation [0.0]
  Estimating physical parameters from data is a crucial application of machine learning (ML) in the physical sciences.<n>We introduce a novel approach based on Contrastive Normalizing Flows (CNFs), which achieves top performance on the HiggsML Uncertainty Challenge dataset.
  arXiv  Detail & Related papers  (2025-05-13T16:14:34Z)
• FUSE: Fast Unified Simulation and Estimation for PDEs [11.991297011923004]
  We argue that solving both problems within the same framework can lead to consistent gains in accuracy and robustness. We present the capabilities of the proposed methodology for predicting continuous and discrete biomarkers in full-body haemodynamics simulations.
  arXiv  Detail & Related papers  (2024-05-23T13:37:26Z)
• Seeing Unseen: Discover Novel Biomedical Concepts via Geometry-Constrained Probabilistic Modeling [53.7117640028211]
  We present a geometry-constrained probabilistic modeling treatment to resolve the identified issues. We incorporate a suite of critical geometric properties to impose proper constraints on the layout of constructed embedding space. A spectral graph-theoretic method is devised to estimate the number of potential novel classes.
  arXiv  Detail & Related papers  (2024-03-02T00:56:05Z)
• Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference [1.1383507019490222]
  Surrogate models are conceptual approximations for more complex simulation models.<n> quantifying and propagating the uncertainty of surrogates is usually limited to special analytic cases.<n>We present three methods for Bayesian inference with surrogate models given measurement data.
  arXiv  Detail & Related papers  (2023-12-08T16:31:52Z)
• Nonparametric Identifiability of Causal Representations from Unknown Interventions [63.1354734978244]
  We study causal representation learning, the task of inferring latent causal variables and their causal relations from mixtures of the variables. Our goal is to identify both the ground truth latents and their causal graph up to a set of ambiguities which we show to be irresolvable from interventional data.
  arXiv  Detail & Related papers  (2023-06-01T10:51:58Z)
• Identification and multiply robust estimation in causal mediation analysis across principal strata [7.801213477601286]
  We consider assessing causal mediation in the presence of a post-treatment event. We derive the efficient influence function for each mediation estimand, which motivates a set of multiply robust estimators for inference.
  arXiv  Detail & Related papers  (2023-04-20T00:39:20Z)
• Evaluating Sensitivity to the Stick-Breaking Prior in Bayesian Nonparametrics [85.31247588089686]
  We show that variational Bayesian methods can yield sensitivities with respect to parametric and nonparametric aspects of Bayesian models. We provide both theoretical and empirical support for our variational approach to Bayesian sensitivity analysis.
  arXiv  Detail & Related papers  (2021-07-08T03:40:18Z)
• BayesIMP: Uncertainty Quantification for Causal Data Fusion [52.184885680729224]
  We study the causal data fusion problem, where datasets pertaining to multiple causal graphs are combined to estimate the average treatment effect of a target variable. We introduce a framework which combines ideas from probabilistic integration and kernel mean embeddings to represent interventional distributions in the reproducing kernel Hilbert space.
  arXiv  Detail & Related papers  (2021-06-07T10:14:18Z)
• Latent Causal Invariant Model [128.7508609492542]
  Current supervised learning can learn spurious correlation during the data-fitting process. We propose a Latent Causal Invariance Model (LaCIM) which pursues causal prediction.
  arXiv  Detail & Related papers  (2020-11-04T10:00:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.