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

A team of researchers from Caltech, UC Irvine, and Harbin Institute of Technology have published a paper on arXiv proposing a new Bayesian inversion framework that uses Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs) to infer discrete structural component states. The work addresses a fundamental challenge in structural health monitoring: determining the health condition of individual components in bridges, buildings, or other infrastructure from measurable responses like vibrations or strains. Traditional Bayesian methods struggle here because the likelihood function linking discrete states to responses is analytically intractable, and the high-dimensional state space (thousands of components) makes marginal likelihood computation prohibitively expensive.

The team's key innovation is modeling the problem as a Markov network, where model parameters are learned from data and structural topology priors. They prove that inference on this PGM yields the same probabilistic estimates as the full Bayesian posterior, effectively sidestepping the likelihood function challenge. To perform inference at scale, they deploy GNNs with a novel graph property-based training strategy that allows the model to generalize across different graph sizes and topologies. This means the same trained GNN can handle structures with varying numbers of components without retraining, dramatically reducing computational overhead. The framework was validated on both synthetic datasets and experimental data from real structural components, showing accurate state inference even in high-dimensional scenarios.