Probabilistic Graphical Model using Graph Neural Networks for Bayesian Inversion of Discrete Structural Component States

• URL: http://arxiv.org/abs/2604.23514v2
• Date: Wed, 29 Apr 2026 07:50:08 GMT
• Title: Probabilistic Graphical Model using Graph Neural Networks for Bayesian Inversion of Discrete Structural Component States
• Abstract summary: This study proposes a novel Bayesian paradigm for discrete variables based on Probabilistic Graphical Models (PGMs)<n>The inference is accomplished by Graph Neural Networks (GNNs), and a graph property-based GNN training strategy is developed to enable accurate inference across varying graph scales.
• Score: 4.25514649547277
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The health condition of components in civil infrastructures can be described by various discrete states according to their performance degradation. Inferring these states from measurable responses is typically an ill-posed inverse problem. Although Bayesian methods are well-suited to tackle such problems, computing the posterior probability density function (PDF) presents challenges. The likelihood function cannot be analytically formulated due to the unclear relationship between discrete states and structural responses, and the high-dimensional state parameters resulting from numerous components severely complicates the computation of the marginal likelihood function. To address these challenges, this study proposes a novel Bayesian inversion paradigm for discrete variables based on Probabilistic Graphical Models (PGMs). The Markov networks are employed as modeling tools, with model parameters learned from data and structural topology prior. It has been proved that inferring this PGM produces the same probabilistic estimation as the posterior PDF derived from Bayesian inference, which effectively solves the above challenges. The inference is accomplished by Graph Neural Networks (GNNs), and a graph property-based GNN training strategy is developed to enable accurate inference across varying graph scales, thereby significantly reducing the computational overhead in high-dimensional problems. Both synthetic and experimental data are used to validate the proposed framework

Related papers

• From Mice to Trains: Amortized Bayesian Inference on Graph Data [2.809401516758154]
  Inference on graph-structured data requires methods that are permutation-invariant, scalable across varying sizes and sparsities, and capable of capturing complex long-range dependencies.<n>ABI is a simulation-based framework that employs generative neural networks to enable fast, likelihood-free posterior inference.
  arXiv  Detail & Related papers  (2026-01-05T16:16:28Z)
• Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning [26.3914014514629]
  In scientific domains -- from biology to the social sciences -- many questions boil down to textitWhat effect will we observe if we intervene on a particular variable?<n>We propose using meta-learning to create an end-to-end model: the Model-Averaged Causal Estimation Transformer Neural Process (MACE-TNP)<n>Our work establishes meta-learning as a flexible and scalable paradigm for approximating complex Bayesian causal inference.
  arXiv  Detail & Related papers  (2025-07-07T22:48:32Z)
• Generative Flow Networks: Theory and Applications to Structure Learning [7.6872614776094]
  This thesis studies the problem of structure learning from a Bayesian perspective.<n>It introduces Generative Flow Networks (GFlowNets)<n>GFlowNets treat generation as a sequential decision making problem.
  arXiv  Detail & Related papers  (2025-01-09T17:47:17Z)
• Estimating Causal Effects from Learned Causal Networks [56.14597641617531]
  We propose an alternative paradigm for answering causal-effect queries over discrete observable variables. We learn the causal Bayesian network and its confounding latent variables directly from the observational data. We show that this emphmodel completion learning approach can be more effective than estimand approaches.
  arXiv  Detail & Related papers  (2024-08-26T08:39:09Z)
• Graph Structure Learning with Interpretable Bayesian Neural Networks [10.957528713294874]
  We introduce novel iterations with independently interpretable parameters. These parameters influence characteristics of the estimated graph, such as edge sparsity. After unrolling these iterations, prior knowledge over such graph characteristics shape prior distributions. Fast execution and parameter efficiency allow for high-fidelity posterior approximation.
  arXiv  Detail & Related papers  (2024-06-20T23:27:41Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  We present a unifying perspective on recent results on ridge regression.<n>We use the basic tools of random matrix theory and free probability, aimed at readers with backgrounds in physics and deep learning.<n>Our results extend and provide a unifying perspective on earlier models of scaling laws.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Equivariant Neural Network for Factor Graphs [83.26543234955855]
  We propose two inference models: Factor-Equivariant Neural Belief Propagation (FE-NBP) and Factor-Equivariant Graph Neural Networks (FE-GNN) FE-NBP achieves state-of-the-art performance on small datasets while FE-GNN achieves state-of-the-art performance on large datasets.
  arXiv  Detail & Related papers  (2021-09-29T06:54:04Z)
• Parameter Estimation with Dense and Convolutional Neural Networks Applied to the FitzHugh-Nagumo ODE [0.0]
  We present deep neural networks using dense and convolutional layers to solve an inverse problem, where we seek to estimate parameters of a Fitz-Nagumo model. We demonstrate that deep neural networks have the potential to estimate parameters in dynamical models and processes, and they are capable of predicting parameters accurately for the framework.
  arXiv  Detail & Related papers  (2020-12-12T01:20:42Z)
• Probabilistic Circuits for Variational Inference in Discrete Graphical Models [101.28528515775842]
  Inference in discrete graphical models with variational methods is difficult. Many sampling-based methods have been proposed for estimating Evidence Lower Bound (ELBO) We propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN) We show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is aweighted the corresponding ELBO can be computed analytically.
  arXiv  Detail & Related papers  (2020-10-22T05:04:38Z)
• Probabilistic Numeric Convolutional Neural Networks [80.42120128330411]
  Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. We propose Probabilistic Convolutional Neural Networks which represent features as Gaussian processes (GPs) We then define a convolutional layer as the evolution of a PDE defined on this GP, followed by a nonlinearity. In experiments we show that our approach yields a $3times$ reduction of error from the previous state of the art on the SuperPixel-MNIST dataset and competitive performance on the medical time2012 dataset PhysioNet.
  arXiv  Detail & Related papers  (2020-10-21T10:08:21Z)
• Structural Causal Models Are (Solvable by) Credal Networks [70.45873402967297]
  Causal inferences can be obtained by standard algorithms for the updating of credal nets. This contribution should be regarded as a systematic approach to represent structural causal models by credal networks. Experiments show that approximate algorithms for credal networks can immediately be used to do causal inference in real-size problems.
  arXiv  Detail & Related papers  (2020-08-02T11:19:36Z)

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.