FSU Mathematics
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Feng Bao Associate Professor Timothy Gannon Endowed Professor Department of Mathematics Florida State University Email: bao@math.fsu.edu Office: LOVE Building 312
I am the Timothy Gannon Endowed Associate Professor of Mathematics at Florida State University. My research interests include data assimilation and stochastic inference, stochastic optimal control, mathematics for machine learning, and uncertainty quantification. In addition to receiving the NSF CAREER Award in 2022, I serve as the PI (or institutional PI) of six major DOE projects, including those that won the DOE AI for Science Call in both 2021 and 2024.
You can find out more about me from some recent FSU spotlight stories: https://artsandsciences.fsu.edu/spectrum-winter-2025/article/advancing-ai https://artsandsciences.fsu.edu/article/faculty-spotlight-feng-bao
Ph.D. in Mathematics, Auburn University, Auburn, USA M.S. in Mathematics, Shandong University, Shandong, China B.S. in Mathematics, Zhejiang University, Hangzhou, China
Florida State University, USA Associate Professor, Department of Mathematics, 2023 - present Florida State University, USA Assistant Professor, Department of Mathematics, 2018 - 2023 University of Tennessee at Chattanooga, USA Assistant Professor, Department of Mathematics, 2016 - 2018 Oak Ridge National Laboratory, USA Postdoc, Division of Computational Science and Mathematics, 2014-2016
- DyGenAI: Dynamic Generative Artificial Intelligence for Prediction and Control of High-Dimensional Nonlinear Complex Systems (DE-SC0025412) DOE - Advanced Scientific Computing Research (PI, $450,987) - Advanced Multi-Physics Machine Learning for Subsurface Energy Systems Across Scales (DE-SC0024703) DOE - Advanced Scientific Computing Research ($4.9M in total with $844,337 for FSU. Project Co-PI and University PI) - CAREER: An Efficient Computational Framework for Data Driven Feedback Control (DMS-2142672) NSF - CAREER Program (PI, $424,053) - Reliable and Efficient Machine Learning for Leadership Facility Scientific Data Analytics (DE-SC0022297) DOE - Advanced Scientific Computing Research (PI, $301,222) - Frameworks, Algorithms and Scalable Technologies for Mathematics (FASTMath-5) DOE - Advanced Scientific Computing Research (University PI, $345,471)
- Efficient Adaptive Backward SDE Methods for Nonlinear Filtering problems (DMS-1720222) NSF - Computational Mathematics Program (PI, $124,995) - Computational Framework for Unbiased Studies of Correlated Electron Systems (CompFUSE) DOE - Advanced Scientific Computing Research (University PI, $225,000) - Accurate Quantified Mathematical Methods for Neutron and Experimental Sciences (ACUMEN) DOE - Advanced Scientific Computing Research (University PI, $180,914)
- NSF CAREER Award, 2022 - ORAU Ralph E. Powe Junior Faculty Enhancement Award, 2017
- Current Ph.D. students: Ruth Lopez Fajardo, Jingqiao Tang, Ryan Bausback, Ruoyu Hu, Zixiang Xiong, Yuanhang Lu - Former Ph.D. students: Xin Li (2021), data scientist at Citi Bank; Zezhong Zhang (2023), Assistant Professor at Auburn University; Hui Sun (2023), Assistant Professor at Xian Jiaotong Liverpool University; Yunzheng Lyu (2024), data scientist at Wells Fargo Bank; Azaryah Wilson (2024), Assistant Professor at Embry-Riddle Aeronautical University; Wonjin Song (2025), Assistant Professor at University of North Georgia; Siming Liang (2025), PostDoc at Oak Ridge National Laboratory
- Foundations of Data Science - Discrete and Continuous Dynamical System - series S - Numerical Methods for Partial Differential Equations |
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1. S. Liang, R. Hu, F. Bao, R. Archibald, and G. Zhang, An Online Algorithm for Solving Feedback Optimal Control Problems with Partial Observations, Foundations of Data Science, doi.org/10.3934/fods.2025010, 2025.
2. F. Bao, H.G. Chipilski, S. Liang, G. Zhang, and J.S. Whitaker, Nonlinear ensemble filtering with diffusion models: Application to the surface quasi-geostrophic dynamics, Monthly Weather Review, doi.org/10.1175/MWR-D-24-0069.1, 2025.
3. T. Huynh, P. Hoang, G. Zhang, and F. Bao, Joint State-Parameter Estimation for the Reduced Fracture Models via a United Filter Method, Journal of Computational Physics, 538, 114159, 2025.
4. S. Harris, R. Fajardo, A. Puretzky, K. Xiao, F. Bao, and R. Vasudevan, Bayesian state estimation unlocks real-time control in thin film synthesis, Nano Letters, 25(6), 2444-2451, 2025.
5. T. Huynh, F. Bao, P. Hoang, Parameter Estimation for Reduced Fracture Model via a Direct Filter Method, Journal of Machine Learning for Modeling and Computing, 6(1), 23-40, 2025.
6. Y. Liu, A. Bryantseva, M. Stoyanov, F. Bao, and G. Zhang, Diffusion-Based Sparse-Grid Generative Models for Density Estimation, Applied Mathematics for Modern Challenges, 4(2), 365-381, 2024.
7. H. Sun, and F. Bao, Solving high dimensional FBSDE with deep signature techniques with application to nonlinear options pricing, Discrete and Continuous Dynamical Systems - Series B, 30(4), 1083-1105, 2024.
8. A.H.M. Rafid, J. Yin, Y. Geng, S. Liang, F. Bao, L. Ju, and G. Zhang, A Scalable Training-Free Diffusion Model for Uncertainty Quantification, The International Conference for High Performance Computing, Networking, Storage, and Analysis (SC24 Workshop), DOI: 10.1109/SCW63240.2024.00057, 2024.
9. J. Yin, S. Liu, S. Liang, F. Bao, H. G. Chipilski, D. Lu, and G. Zhang, A Scalable Real-Time Data Assimilation Framework for Predicting Turbulent Atmosphere Dynamics, The International Conference for High Performance Computing, Networking, Storage, and Analysis (SC24 Workshop), DOI: 10.1109/SCW63240.2024.00009, 2024.
10. F. Bao, Z. Zhang, and G. Zhang, An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems, Computer Methods in Applied Mechanics and Engineering (CMAME), 432, 117447, 2024.
11. Z. Zhang, F. Bao, and G. Zhang, Improving the expressive power of deep neural networks through integral activation transform, International Journal of Numerical Analysis and Modeling, 21(5), 739-763, 2024.
12. Y. Lyu, and F. Bao, Convergence Analysis of Kernel Learning FBSDE Filter, Communications in Mathematical Research, 40, 313-342, 2024.
13. S. Liang, H. Sun, R. Archibald, and F. Bao, Convergence Analysis for An Online Data Driven Feedback Control Algorithm, Mathematics, 12(16), 2584, 2024.
14. D. Lu, Y. Liu, Z. Zhang, F. Bao, and G. Zhang, A Diffusion-Based Uncertainty Quantification Method to Advance E3SM Land Model Calibration, AGU Journal of Geophysical Research: Machine Learning and Computation, 3(1), e2024JH000234, 2024.
15. F. Bao, Z. Zhang, and G. Zhang, A Score-based Filter for Nonlinear Data Assimilation, Journal of Computational Physics, 514, 113207, 2024.
16. D. Lu, Z. Zhang, F. Bao, and G. Zhang, Advancing Earth System Model Calibration: A Diffusion-Based Method, The Twelfth International Conference on Learning Representations (ICLR24 Workshop), Honorable Mention, 2024.
17. H. Li, S. Yang, H. Chi, L. Xu, T. Zhang, F. Bao, W. Stone, and J. Wang, Functionality and Feasibility of Cognitive Function Training via Mobile Health Application Among Youth at Risk for Psychosis, Exploration of Digital Health Technologies, 7(2), 7-19, 2024.
18. Z. Zhang, F. Bao, L. Ju, and G. Zhang, TransNet: Transferable Neural Networks for Parital Differential Equations, Journal of Scientific Computing, 99(2), 2024.
19. Y. Liu, M. Yang, Z. Zhang, F. Bao, Y. Cao, and G. Zhang, Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation, Journal of Machine Learning for Modeling and Computing, 5(1), 25-38, 2024.
20. R. Archibald, F. Bao, Y. Cao, and H. Sun, Numerical Analysis for Convergence of a Sample-wise Back-propagation Method for Training Stochastic Neural Networks, SIAM Journal on Numerical Analysis, 62(2), 593-621, 2024.
21. H. Sun, F. Bao, and N. Moore, Parameter Estimation for the Truncated KdV Model through a Direct Filter Method, Journal of Machine Learning for Modeling and Computing, 4(1), 109-132, 2023.
22. R. Archibald, F. Bao, and J. Yong, An Online Method for Data Driven Stochastic Optimal Control with Unknown Model Parameters, Communications in Computational Physics, 33(4), 1132-1163, 2023.
23. F. Bao, Y. Cao, and H. Zhang, A Splitting-up Scheme for Backward Doubly Stochastic Differential Equations, Advances in Computational Mathematics, 49, 65, 2023.
24. R. Archibald, F. Bao, and J. Yong, A Stochastic Maximum Principle Approach for Reinforcement Learning with Parameterized Environment, Journal of Computational Physics, 488, 112238, 2023.
25. P. Mai, N. Nicholas, S. Karakuzu, F. Bao, A. Maestro, T. Maier and S. Johnston, Robust Charge-density Wave Correlations in the Electron-doped Single-band Hubbard Model, Nature Communications, 14, 2889, 2023.
26. Z. Zhang, R. Archibald, and F. Bao, A PDE-based Adaptive Kernel Method for Solving Optimal Filtering Problems, Journal of Machine Learning for Modeling and Computing, 3(3), 37-59, 2022.
27. O. Dyck, F. Bao, M. Ziatdinov, Ali Y. Nobakht, K. Law, A. Maksov, B.G. Sumpter, R. Archibald, S. Jesse, S.V. Kalinin, and D.B. Lingerfelt, Strain-Induced Asymmetry and Om-Site Dynamics of Silicon Defects in Graphene, Carbon Trends, 9, 100189, 2022.
28. R. Archibald, F. Bao, Y. Cao, and H. Zhang, A Backward SDE Method for Uncertainty Quantification in Deep Learning, Discrete and Continuous Dynamical Systems - Series S, 15(10), 2807-2835, 2022.
29. R. Archibald, and F. Bao, Kernel Learning Backward SDE filter for Data Assimilation, Journal of Computational Physics, 455, 111009, 2022.
30. X. Li, F. Bao, and K. Gallivan, A Drift Homotopy Implicit Particle Filter Method for Nonlinear Filtering Problems, Discrete and Continuous Dynamical Systems - Series S, 15(4), 727-746, 2022
31. X. Xie, F. Bao, T. Maier, and C. Webster, Analytic Continuation of Noisy Data Using Adams Bashforth Residual Neural Network, Discrete and Continuous Dynamical Systems - Series S, 15(4), 877-892, 2022.
32. N.G. Cogan, F. Bao, R. Paus, and A. Dobreva, Data Assimilation of Synthetic Data as a Novel Strategy for Predicting Disease Progression in Alopecia Areata, Mathematical Medicine and Biology: A Journal of the IMA, 06,14778602 2021.
33. H. Sun, and F. Bao, Meshfree Approximation for Stochastic Optimal Control Problems, Communications in Mathematical Research, 37(3), pp. 387-420, 2021.
34. F. Bao, Y. Cao, and J. Yong, Data Informed Solution Estimation for Forward Backward Stochastic Differential Equations, Analysis and Applications, 19(3), pp. 439-464, 2021.
35. O. Dyck, M. Ziatdinov, S. Jesse, F. Bao, A.Y. Nobakht, A. Maksov, S. Shin, B.G. Sumpter, R. Archibald, K.J.H. Law, and S.V. Kalinin, Probing potential energy landscapes via electron-beam-induced single atom dynamics, Acta Materialia, 203, 116508, 2021.
36. R. Archibald, F. Bao, J. Yong, and T. Zhou, An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems, Journal of Scientific Computing, 85-51, 2020.
37. A.Y. Nobakht, O. Dyck, D.B. Lingerfelt, F. Bao, M. Ziatdinov, A. Maksov, B.G. Sumpter, R. Archibald, S. Jesse, S.V. Kalinin, and K.J.H. Law, Reconstruction of Effective potential from statistical analysis of dynamic trajectories, AIP Advances, 10(6), 065034, 2020.
38. R. Archibald, F. Bao, and J. Yong, A Stochastic Gradient Descent Approach for Stochastic Optimal Control, East Asian Journal of Applied Mathematics, 10(4), 635-658, 2020.
39. F. Bao, Y. Cao and X. Han, Forward Backward Doubly Stochastic Differential Equations and Optimal Filtering of Diffusion Processes, Communications in Mathematical Sciences, 18(3), 635-661, 2020.
40. F. Bao and T. Maier, Stochastic Gradient Descent Algorithm for Stochastic Optimization in Solving Analytic Continuation Problems, AIMS Foundations of Data Science, 2(1), 1-17, 2020.
41. F. Bao, R. Archibald and P. Maksymovych, Backward SDE Filter for Jump Diffusion Processes and Its Applications in Material Sciences, Communications in Computational Physics, (27), 589-618, 2020.
42. R. Archibald, R. Bao and X. Tu, A Direct Filter Method for Parameter Estimation, Journal of Computational Physics, (398), 108871, 2019.
43. F. Bao and Y. Cao, Adjoint Forward Backward Stochastic Differential Equations Driven by Jump Processes and Its Application to Nonlinear Filtering Problems, International Journal for Uncertainty Quantification, 9(2), 143-159, 2019.
44. F. Bao, L. Mu and J. Wang, A Fully Computable Posteriori Error Estimation for the Stokes Equations on Polytopal Meshes, SIAM Journal on Numerical Analysis, 57(1), 458-477, 2019.
45. O. Dyck, F. Bao, M. Ziatdinov, A. Y. Nobakht, S. Shin, K. Law, A. Maksov, B.G. Sumpter, R. Archibald, S. Jesse, and S.V. Kalinin, Leveraging Single Atom Dynamics to Measure the Electron-Beam-Induced Force and Atomic Potentials, Proceedings of Microscopy and Microanalysis, 24, pp. 96-97, 2018.
46. X. Xie, F. Bao and C. Webster, Evolve Filter Stabilization Reduced-Order Model for Stochastic Burgers Equation, Fluids, 3(4), 3040084, 2018.
47. C. Yang, D. Posny, F. Bao and J. Wang, A Multi-scale Cholera Model Linking Between-host and Within-host Dynamics, International Journal of Biomathematics, 11(3), 1850034, 2018.
48. F. Bao, Y. Cao and W. Zhao, A Backward Doubly Stochastic Differential Equation Approach for Nonlinear Filtering Problems, Communications in Computational Physics, 23(5), pp. 1573-1601, 2018.
49. K. Kang, V. Maroulas, I. Schizas and F. Bao, Improved Distributed Particle Filters for Tracking in Wireless Sensor Network, Computational Statistics and Data Analysis, 117: 90-108, 2018.
50. F. Bao and V. Maroulas, Adaptive Meshfree Backward SDE Filter, SIAM Journal on Scientific Computing, 39(6), A2664-A2683, 2017.
51. F. Bao, Y. Cao, X. Han and J. Li, Efficient Particle Filtering for Stochastic Korteweg-De Vries Equations, Stochastics and Dynamics, 17(2),1750008, 2017.
52. F. Bao, R. Archibald, J. Niedziela, D. Bansal and O. Delaire, Complex Optimization for Big Computational and Experimental Neutron Datasets, Nanotechnology, 27(48), 484002, 2016.
53. F. Bao, Y. Tang, M. Summers, G. Zhang, C. Webster, V. Scarola and T.A. Maier, Fast and Efficient Stochastic Optimization for Analytic Continuation, Physical Review-B, 94: 125149, 2016.
54. F. Bao, R. Archibald, D. Bansal and O. Delaire, Hierarchical Optimization for Neutron Scattering Problems, Journal of Computational Physics, 315: 39-51, 2016.
55. F. Bao, Y. Cao, C. Webster and G. Zhang, An Efficient Meshfree Implicit Filter for Nonlinear Filtering Problems, International Journal for Uncertainty Quantification, 6(1), 19-33 2016.
56. F. Bao, Y. Cao, A. Meir and W. Zhao, A First Order Fully Discretized Numerical Algorithm for Backward Doubly Stochastic Differential Equations, SIAM/ASA Journal on Uncertainty Quantification, 4(1), 413-445, 2016.
57. B. Hu, Y. Cao, W. Zhao and F. Bao, Identification of hydraulic conductivity distributions in density dependent flow fields of submarine groundwater discharge modelling using adjoint-state sensitivities, SCIENCE CHINA Earth Sciences, 59(4): 770-779, 2016.
58. F. Bao, Y. Cao and W. Zhao, A First Order Semi-Discrete Algorithm for Backward Doubly Stochastic Differential Equations, Discrete and Continuous Dynamical Systems - Series B, 2(5), pp. 1297-1313, 2015.
59. F. Bao, Y. Cao, C. Webster and G. Zhang, A Hybrid Sparse-Grid Approach for Nonlinear Filtering Problems Based on Adaptive-Domain of the Zakai Equation Approximations, SIAM/ASA Journal on Uncertainty Quantification, 2(1), pp.784-804, 2014.
60. F. Bao, Y. Cao and X. Han, An Implicit Algorithm of Solving Nonlinear Filtering Problems, Communications in Computational Physics, 16(2), pp. 382-402, 2014.
61. F. Bao, Y. Cao and W. Zhao, Numerical Solutions for Forward Backward Doubly Stochastic Differential Equations and Zakai Equations, International Journal for Uncertainty Quantification, 1(4), pp. 351-367, 2011.