In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed that incorporate neural networks to enhance their performance for specific Bayesian model updating problems. However, a common challenge with these approaches lies in the fact that the embedded neural networks often necessitate retraining when faced with new tasks, a process that is time-consuming and significantly undermines the competitiveness of these methods. This paper introduces a newly developed adaptive meta-learning stochastic gradient Hamiltonian Monte Carlo (AM-SGHMC) algorithm. The idea behind AM-SGHMC is to optimize the sampling strategy by training adaptive neural networks, and due to the adaptive design of the network inputs and outputs, the trained sampler can be directly applied to various Bayesian updating problems of the same type of structure without further training, thereby achieving meta-learning. Additionally, practical issues for the feasibility of the AM-SGHMC algorithm for structural dynamic model updating are addressed, and two examples involving Bayesian updating of multi-story building models with different model fidelity are used to demonstrate the effectiveness and generalization ability of the proposed method.

A neural network (cf. Figure 1) can be thought of as a directed acyclic network consisting of

This rich view shows which parameters are responsible for decreasing or increasing the loss during training, orwhich parameters "help" or"hurt" the network'slearning, respectively.

Neural network training is usually accomplished by solving a non-convex optimization problem using stochastic gradient descent. Although one optimizes over the networks parameters, the main loss function generally only depends on the realization of the neural network, i.e. the function it computes. Studying the optimization problem over the space of realizations opens up new ways to understand neural network training. In particular, usual loss functions like mean squared error and categorical cross entropy are convex on spaces of neural network realizations, which themselves are non-convex. Approximation capabilities of neural networks can be used to deal with the latter non-convexity, which allows us to establish that for sufficiently large networks local minima of a regularized optimization problem on the realization space are almost optimal.

A neural network (cf. Figure 1) can be thought of as a directed acyclic network consisting of