Title: Generative AI for Uncertainty Quantification

Speaker: Guannan Zhang (Oak Ridge National Laboratory)

Abstract: Generative models, including variational autoencoders, normalizing flows, generative adversarial networks, and diffusion models, have dramatically advanced the realism and quality of generated images, text, and audio. Beyond these tasks, generative models hold great promise as powerful tools for probability density estimation and high-dimensional sampling, which are central to uncertainty quantification (UQ) tasks such as amortized Bayesian inference and data assimilation. However, while research on image synthesis emphasizes producing high-quality individual samples, UQ applications require accurate approximation of statistical quantities of interest rather than visually realistic samples. As a result, direct application of existing generative models to UQ problems can lead to biased approximations or unstable training. In this talk, we will introduce several new generative approaches tailored to UQ. These include training-free diffusion models for density estimation, a score-based nonlinear filter for data assimilation, and training-free conditional diffusion models for amortized Bayesian inference. We will demonstrate their effectiveness across a range of tasks, including density estimation for unimodal and multimodal distributions, learning stochastic dynamical systems, parameter estimation via amortized inference, and scalable data assimilation for atmospheric models.