Data-Driven Stochastic Model Updating with Diffusion Models

Stochastic model updating is a vital technique in engineering that can calibrate the input parameters of the computational model to reflect the real-world physical system while accounting for the existence of uncertainties. However, traditional methods such as the Bayesian approach always struggle with high-dimensional and nonlinear problems. Thus, there is a trend to adopt data-driven approaches to solve stochastic model updating problems since of their remarkable capability to process high-dimensionality and nonlinearity. Apart from utilising neural networks as a surrogate for forward models, the conditional invertible neural networks (cINNs), a type of flow-based deep generative model, can serve as an inverse surrogate to address stochastic model updating problems alternatively. Recently, another group of deep generative models called Diffusion Models has become very popular in generation tasks because of their better ability to handle complex distributions, flexibility in network architecture and stability in training. In this work, the feasibility of leveraging diffusion models to resolve stochastic model updating problems is investigated. Diffusion models transform a simple latent distribution (e.g., Gaussian noise) into a complex distribution that aligns with observation data through a gradual iterative process. In contrast to cINNs, diffusion models build up complexity in the learned distribution progressively through a series of Markov chains, allowing for more accurate modelling of complex systems with high uncertainty. A 3 DOF spring-mass system was adopted as an example. The training dataset is formed by input parameters generated from the prior distribution and synthetic observation data obtained from the forward numerical model. This work presents diffusion models as a potential alternative to conventional Bayesian approaches for stochastic model updating, with advantages in accuracy, uncertainty, and flexibility for complicated, real-world applications.

Keywords: Stochastic model updating, Uncertainty analysis, Deep generative models, Machine learning.