Bayesian model updating based on a deep neural network classifier

Designing an appropriate likelihood function is one of the most critical components of Bayesian model updating. Approximate Bayesian computation (ABC) provides an effective framework for such likelihood evaluation in dynamic structural systems, in which both observations and parameters can be complex and high-dimensional. It has been shown that ABC can effectively evaluate the likelihood; however, some challenges still exist, such as the high computational cost within Markov chain Monte Carlo (MCMC). Recently, several studies have introduced deep generative models, such as variational autoencoders and normalizing flows, into the Bayesian model updating framework. A key advantage of these models is their ability to learn unknown probability distributions from data and to serve as likelihood estimators. This study proposes a novel Bayesian model updating framework that utilizes the discriminator of generative adversarial networks (GAN). In our previous study, we developed several GAN-based models that generate ground-motion time history data and showed that the discriminators can precisely capture the characteristics of such time series and evaluate their distributions. Building on this foundation, by developing a classifier model using deep neural networks, we propose a likelihood-free method for Bayesian model updating capable of handling high-dimensional data. In the proposed method, the relationship between observations and parameters is modeled by the classifier, eliminating the need for explicit likelihood modeling and removing the requirement for simulator calls during MCMC. The proposed method is presented in detail, and its performance is demonstrated through several numerical experiments, including applications to the seismic response of structures.