段金桥

段金桥（1962年12月），中国应用数学家，大学教授。特别专长于随机动力系统，非线性动力系统与随机偏微分方程及其在数据科学，生物物理和地球物理系统中的应用。他在随机动力系统不变流形理论、有效约化与逼近方法，Onsager-Machlup 作用泛函理论和亚稳态之间的迁移规律，非高斯噪声与非局部偏微分方程，非局部Kramers-Moyal公式，非高斯噪声的动态影响与非高斯数据同化（data assimilation）等领域做出重要贡献, 并应用于一些生物物理和地球物理系统。最近，他也在进行随机动力系统与数据科学的交叉研究，并提出非局部Kramers-Moyal公式用于从数据中提取随机控制律。他还在从事随机Hamilton/Contact系统与随机几何力学，量子开放系统与随机动力系统的交叉研究。

他曾任美国国家纯粹与应用数学研究所副所长（挂靠在加州大学洛杉矶分校），曾任美国国家基金委一个数据科学研究所轮值所长与分所长，还曾被聘为美国密苏里科技大学冠名Gary Havener系主任。

他本科毕业于武汉大学计算数学专业，硕士毕业于中国科学院（数学物理研究方向），又硕士毕业于马萨诸塞大学阿默斯特分校，博士毕业于康奈尔大学应用数学中心（动力系统研究领域，导师菲利普·霍尔姆斯）。他随后在加州理工学院跟随Stephen Wiggins 做博士后与Instructor。

他先后在加州理工学院、克莱门森大学、加州大学洛杉矶分校和伊利诺理工学院任教。

现任大湾区大学讲席教授兼理学院执行院长。

## 科学贡献

段金桥教授的研究领域包括随机动力系统与非线性动力系统理论、计算和模拟, 以及数学与其它学科的交叉研究(地球与环境、生命科学等有关的随机现象与复杂现象)。段金桥教授在非高斯随机动力系统，随机偏微分方程齐性化及其相关应用研究领域作出了重要贡献，并获得多项科研基金和科研奖励。

他现任Stochastics and Dynamics (“随机动力系统”) 杂志管理编辑。

他还任Interdisciplinary Mathematical Sciences (“跨学科应用数学丛书”) 主编，以及“Nonlinear Processes in Geophysics”编委。

## 部分出版

- Jinqiao Duan, Kening Lu, Björn Schmalfuss. "Invariant manifolds for stochastic partial differential equations," The Annals of Probability, Ann. Probab. 31(4), 2109-2135, (October 2003)
- D. Schertzer and M. Larchevêque, J. Duan, V. V. Yanovsky, S. Lovejoy. "Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises", J. Math. Phys. 42, 200-212 (2001) https://doi.org/10.1063/1.1318734
- Yang Li, Jinqiao Duan. "A data-driven approach for discovering stochastic dynamical systems with non-Gaussian Lévy noise", Physica D: Nonlinear Phenomena, Volume 417, 2021, 132830, ISSN 0167-2789, https://doi.org/10.1016/j.physd.2020.132830
- Yubin Lu, Yang Li and Jinqiao Duan. "Extracting stochastic governing laws by non-local Kramers–Moyal formulae", Phil. Trans. R. Soc. A.380: 20210195. 20210195 http://doi.org/10.1098/rsta.2021.0195
- Wei Wei, Ting Gao, Xiaoli Chen, and Jinqiao Duan, An optimal control method to compute the most likely transition path for stochastic dynamical systems with jumps. Chaos 32, 051102 (2022); https://doi.org/10.1063/5.009392
- Jianyu Hu, Dongfang Li, Jinqiao Duan and Xiaoli Chen, Data-driven method to learn the most probable transition pathway and stochastic differential equations, Physica D, 2023. https://doi.org/10.1016/j.physd.2022.133559
- Jintao Wang, Desheng Li, Jinqiao Duan, Compactly generated shape index theory and its application to a retarded nonautonomous parabolic equation. Topological Methods in Nonlinear Analysis. Volume 59, No. 1, 2022, 1-33. DOI: 10.12775/TMNA.2021.031
- Y. Li and J. Duan, Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic Dynamical Systems. Journal of Statistical Physics (2022) 186:30.
- Dandan Li, Jinqiao Duan, Li Lin, and Ao Zhang, Bohmian trajectories of the time-oscillating Schringer equations Chaos 31, 101101 (2021); https://doi.org/10.1063/5.0067645
- Huang, Yuanfei; Chao, Ying; Wei, Wei; and Duan, Jinqiao, Estimating the Most Probable Transition Time for Stochastic Dynamical Systems. Nonlinearity, 2021, vol. 34, 4543.
- Qi Zhang and J. Duan, Linear Response Theory for Nonlinear Stochastic Differential Equations with α–stable Lévy Noises. Journal of Statistical Physics 182, 32 (2021).
- Xiaoli Chen, Jinqiao Duan and George Em Karniadakis, Learning and Meta-Learning of Stochastic Advection-Diffusion-Reaction Systems from Sparse Measurements. European J. Appl. Math., 15 June 2020. doi:10.1017/S0956792520000169
- A. Zhang and J. Duan, Effective Wave Factorization for a Stochastic Schrödinger Equation. Physica D, Volume 411, October 2020, 132573. https://doi.org/10.1016/j.physd.2020.132573
- Yayun Zheng, Fang Yang, Jinqiao Duan, Xu Sun, Ling Fu and Jürgen Kurths, The maximum likelihood climate change for global warming under the influence of greenhouse effect and Lévy noise. Chaos, 30, 013132 (2020); https://doi.org/10.1063/1.5129003.
- Fang Yang, Yayun Zheng, Jinqiao Duan, Ling Fu and Stephen Wiggins, The tipping times in an Arctic sea ice system under influence of extreme events. Chaos 30, 063125 (2020).
- Ying Chao and Jinqiao Duan, The Onsager-Machlup function as Lagrangian for the most probable path of a jump-diffusion process. Nonlinearity, 32 (2019) 3715 - 3741.
- S. Yuan and J. Duan, Action Functionals for Stochastic Differential Equations with Lévy Noise. Communications on Stochastic Analysis, Vol 13, No. 3, 2019, Article 10. DOI: 10.31390/cosa.13.3.10
- H. Qiao, Y. Zhang and J. Duan. Effective filtering on a random slow manifold. Nonlinearity 31 (2018) 4649-4666
- Wei Zou, D. V. Senthilkumar, Raphael Nagao, Istvan Z. Kiss, Yang Tang, Aneta Koseska, Jinqiao Duan and Jurgen Kurths, Restoration of rhythmicity in diffusively coupled dynamical networks. Nature - Communications July 15, 2015. DOI: 10.1038/ncomms8709

## 书籍

- An Introduction to Stochastic Dynamics, Cambridge University Press, 2015.
- Effective Dynamics of Stochastic Partial Differential Equations (with Wei Wang), Elsevier, 2014.
- Probability and Partial Differential Equations in Modern Applied Mathematics (with E. Waymire, Eds.), Springer-Verlag, 2005.
- Recent Development in Stochastic Dynamics and Stochastic Analysis (with S. Luo and C. Wang, Eds.), World Scientific, New Jersey, 2010.

## 基本资料

- 出生日期：1962年
- 教育程度：博士
- 知名原因：随机动力系统、随机偏微分方程
- 研究领域：应用数学与跨学科研究
- 机构：加州理工学院、加州大学洛杉矶分校、华中科技大学、伊利诺理工学院、大湾区大学
- 母校：康奈尔大学、麻省大学阿默斯特分校、中国科学院、武汉大学
- 博士导师：菲利普·霍尔姆斯