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

Publications:

1. 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. (https://arxiv.org/abs/2508.06834)

2. M. Yang, Y. Liu, D. del-Castillo-Negrete, Y. Cao, G. Zhang, Generative AI Models for Learning Flow Maps of Stochastic Dynamical Systems in Bounded Domains, submitted (http://arxiv.org/abs/2507.15990).

3. Z. Zhang, C. Tatsuoka, D. Xiu, G. Zhang, Exact conditional score-guided generative modeling for amortized inference in uncertainty quantification, submitted (https://arxiv.org/abs/2506.18227). 

4. H. Tran, Z. Zhang, F. Bao, D. Lu, G. Zhang, Diffusion-based supervised learning of generative models for efficient sampling of multimodal distributions, submitted (https://arxiv.org/abs/2505.07825). 

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

6. C. Tatsuoka, M. Yang, D. Xiu, G. Zhang, Multi-fidelity Parameter Estimation Using Conditional Diffusion Models, submitted (https://arxiv.org/abs/2504.01894). 

7. 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 (https://arxiv.org/abs/2501.12419). 

8. Y. Liu, Y. Chen, D. Xiu, G. Zhang, A training-free conditional diffusion model for learning stochastic dynamical systems, SIAM Journal on Scientific Computing, accepted, 2025 (https://arxiv.org/abs/2410.03108).

9. 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)

10. M. Fan, Z. Zhang, D. Lu, G. Zhang, GenAI4UQ: A software for inverse uncertainty quantification using conditional generative AI models, SoftwareX, 31, 102232, 2025 (DOI: 10.1016/j.softx.2025.102232).

11. 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).

12. 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)

13. 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)

14. Y. Liu, A. Bryantseva, M. Stoyanov, F. Bao, G. Zhang, Diffusion-based sparse-grid generative models for density estimation,  Applied Mathematics for Modern Challenges, 2(4), pp. 365-381, 2024. (DOI: 10.3934/ammc.2024019)

15. M. Fan, Y. Liu, D. Lu, H. Wang, G. Zhang, A novel conditional generative model for efficient ensemble forecasts of state variables in large-scale geological carbon storage, Journal of Hydrology, 648, 132323, 2025. (DOI: 10.1016/j.jhydrol.2024.132323)

16. 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)

17. D. Lu, Y. Liu, Z. Zhang, F. Bao, G. Zhang, A diffusion-based uncertainty quantification method to advance E3SM model calibration, Journal of Geophysical Research: Machine Learning and Computation, 1,  e2024JH000234, 2024. (DOI:10.1029/2024JH000234)

18. 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)

19. Y. Liu, M. Yang, Z. Zhang, F. Bao, Y. Cao, G. Zhang, Diffusion-model-assisted supervised learning of generative models for density estimation, Journal of Machine Learning for Modeling and Computing, 5(1), pp. 25-38, 2024. (DOI:10.1615/JMachLearnModelComput.2024051346)