Project description: 

Generative artificial intelligence (AI) is evolving from image synthesis to a vital uncertainty quantification tool for learning complex high-dimensional probability distributions. Particularly within the U.S. Department of Energy (DOE), integrating generative AI as an outer-loop with physics-based or AI foundation models can significantly enhance decision-making. However, a gap exists as current generative AI models are static, limiting their effectiveness in the DOE’s dynamic mission areas like energy distribution and extreme events monitoring. This project will develop a dynamic generative artificial intelligence (DyGenAI) paradigm to transform the generative AI methodology from a static paradigm into a dynamic paradigm, enhancing computational efficiency and adaptability to real-time changes. The research is structured around three thrusts: developing training-free diffusion models for Bayesian inference, extending these models for stochastic control, and accelerating these algorithms on supercomputers for real-time applications. This will be demonstrated in predictive models for atmospheric turbulence and plasma control in fusion reactors, aiming to improve AI trustworthiness, energy system reliability, and support informed decision-making in energy security.

Sponsor: DOE, Advanced Scientific Computing Research (ASCR)

Funding period: 2024 -- 2027

Team: Oak Ridge National Laboratory (Lead), Sandia National Laboratories, Columbia University, Florida State University, Auburn University, University of South Carolina

Accepted papers and pre-prints

• B. Shi, L. Zhang, and Q. Du, Stochastic saddle search with convergence guarantee, submitted to SIAM J Numer. Anal., 2025 (https://arxiv.org/abs/2510.14144)

• L. Lan, S. Billinge, and Q. Du, A continuous symmetry-breaking measure for finite clusters using Jensen-Shannon divergence, submitted to Physical Review X, 2025. (https://arxiv.org/abs/2410.21880)

• D. Lin, and Q. Du, Nonlinear optimal recovery in Hilbert spaces, submitted to Analysis and Approximation, 2025 (https://arxiv.org/abs/2506.00704)

• Q. Du,  K. Wang, E. Zhang, and  C. Zhong, A Particle Algorithm for Mean-Field Variational Inference, submitted to SIAM J. Optimization (under revision), 2025 (https://arxiv.org/abs/2412.20385)

• Z. Zhang, F. Bao, G. Zhang, IEnSF: Iterative Ensemble Score Filter for Reducing Error in Posterior Score Estimation in Nonlinear Data Assimilation, submitted, 2025 (https://arxiv.org/abs/2510.20159)

• Y. Geng, J. Yin, E. C. Cyr, G. Zhang, L. Ju, Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method, submitted, 2025 (https://arxiv.org/abs/2510.07672)

• T. Huynh, R. Fajardo, G. Zhang, L. Ju, F. Bao, A Score-based Diffusion Model Approach for Adaptive Learning of Stochastic Partial Differential Equation Solutions, submitted, 2025 (https://arxiv.org/abs/2508.06834)

• S. Liang, H. Tran, F. Bao, H. Chipilski, P.J. van Leeuwen, G. Zhang, Ensemble score filter with image inpainting for data assimilation in tracking surface quasi-geostrophic dynamics with partial observations, submitted, 2025 (https://arxiv.org/abs/2501.12419).

• Z. Xiong, S. Liang, F. Bao, G. Zhang, H. Chipilski, On the sensitivity of different ensemble filters to the type of assimilated observation networks, Atmospheric Research Letters, accepted, 2025  (https://arxiv.org/abs/2505.04541)

• Y. Liu, Y. Cao, and J. Lin, Convergence Analysis of the ADAM Algorithm for Linear Inverse Problems, Applied Numerical Mathematics, to appear, 2025.

• F. Bao, Z. Zhang, G. Zhang, A unified filter method for jointly estimating state and parameters of stochastic dynamical systems via the ensemble score filter, Communications in Computational Physics, accepted, 2024. (https://arxiv.org/abs/2312.10503)

Journal Articles

• H. Qian , Y. Cao , and G. Yin, Large deviation estimates for nonlinear filtering with discontinuity and small noise.  Stochastic Processes and their Applications 187, 104662, 2025

• T. Huynh, T. Hoang, G. Zhang, F. Bao, Joint State-Parameter Estimation for the Reduced Fracture Model via the United Filter, Journal of Computational Physics, 538, 114159, 2025. (DOI: 10.1016/j.jcp.2025.114159)

• S. Liang, R. Hu, F. Bao, R. Archibald, G. Zhang, Assimilating Partial Observation to Enhance Feedback Control of Stochastic Dynamical Systems, Foundations of Data Science, 2025 (DOI: 10.3934/fods.2025010).

• F. Bao, H. Chipilski, S. Liang, G. Zhang, J. Whitaker, Nonlinear ensemble filtering with diffusion models: application to the surface quasi-geostrophic dynamics, Monthly Weather Review, 153(7), pp. 1155–1169, 2025. (DOI: 10.1175/MWR-D-24-0069.1)

• T. Huynh, T. Hoang, G. Zhang, F. Bao, Joint State-Parameter Estimation for the Reduced Fracture Model via the United Filter, Journal of Computational Physics, 538, 114159, 2025. (DOI: 10.1016/j.jcp.2025.114159)

• F. Bao, Z. Zhang, G. Zhang, An ensemble score filter for tracking high-dimensional nonlinear dynamical system, Computer Methods in Applied Mechanics and Engineering, 432, Part B, 117447, 2024. (DOI:10.1016/j.cma.2024.117447)

• F. Bao, Z. Zhang, G. Zhang, A score-based filter for nonlinear data assimilation, Journal of Computational Physics, 514, 113207, 2024. (DOI:10.1016/j.jcp.2024.113207)

Conference Proceedings

• Z. Wang, S. Mao, F. Bao, and Y. Cao, TF-Diff: Training-free Diffusion for Cross-Domain RF-based Human Activity Recognition, IEEE Global Communications Conference, 2025.

• J. Yin, S. Liang, S. Liu, F. Bao, H. Chipilski, D. Lu, G. Zhang, A Scalable Real-Time Data Assimilation Framework for Predicting Turbulent Atmosphere Dynamics, Proceedings of the SC '24 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis, 2024. [Download, DOI:10.1109/SCW63240.2024.00009]