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

2026-04-25

AI Summary

This study addresses the high-dimensional, ill-posed Bayesian inverse problem of inferring discrete component states in civil infrastructure, which is hindered by intractable likelihood functions and prohibitive computational costs. To overcome these challenges, the authors propose a novel Bayesian inversion framework that integrates Markov random fields with graph neural networks, leveraging structural topology as a prior. A graph attribute–guided training strategy enables efficient posterior estimation while preserving physical interpretability. The method demonstrates robust cross-scale inference accuracy on both synthetic and experimental datasets, significantly reducing computational overhead and effectively alleviating the scalability limitations inherent in conventional Bayesian approaches when applied to complex infrastructure systems.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Graphical Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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

Problem

• Bayesian inversion
• discrete states
• ill-posed inverse problem
• high-dimensional inference
• structural health monitoring

Innovation

• Probabilistic Graphical Model
• Graph Neural Networks
• Bayesian Inversion
• Discrete Structural States
• Markov Networks