Stochastic model updating using conditional diffusion-based probabilistic generative models

This work aims to explore the integration of novel and powerful deep learning techniques and intractable engineering problems, especially by adopting deep generative models to tackle model updating problems under uncertainty. A conditional denoising diffusion probabilistic model-based updating framework is presented to extend the field of deep generative models-based model updating methods. The diffusion model is a representative generative AI technique that employs a Markov chain to progressively add noise to data (forward process), then train a deep neural network to reverse this corruption (reverse process), enabling high-quality data generation. The conditional denoising diffusion extends the standard diffusion model, which guides data synthesis by injecting conditional inputs into the diffusion process. The conditional diffusion-based model updating framework consists of two primary neural networks: a conditional network and a denoising network. The conditional network can summarise the synthetic/measured response data into an informative fixed-length vector, called a conditional embedding, for guiding the training and denoising process of the denoising network. The denoising network can learn to predict the noise added in the forward process and denoise to generate the posterior samples conditioned on the conditional embedding. Both networks are trained jointly, and their architectures are flexible and problem-dependent. The framework is applied to solve a simulation-based problem, which is a customised version of the NASA and DNV Uncertainty Quantification Challenge 2025, and an experimental case study, which is a recently designed benchmark testbed with both experiment uncertainty and controllable parameter uncertainty.