段金桥

**段金橋**（1962 年 12 月 —），男，中國應用數學家。特別專長於隨機動力系統，非線性動力系統與隨機偏微分方程及其在數據科學，生物物理和地球物理系統中的應用。他在隨機動力系統不變流形理論、有效約化與逼近方法，Onsager-Machlup 作用泛函理論和亞穩態之間的遷移規律，非高斯噪聲與非局部偏微分方程， 非局部 Kramers-Moyal 公式，非高斯噪聲的動態影響與非高斯數據同化（data assimilation) 等領域做出重要貢獻，並應用於一些生物物理和地球物理系統。最近，他也在進行隨機動力系統與數據科學的交叉研究，並提出非局部 Kramers-Moyal 公式用於從數據中提取隨機控制律。他還在從事隨機 Hamilton/Contact 系統與隨機幾何力學，量子開放系統與隨機動力系統的交叉研究。

 
他曾任美國國家純粹與應用數學研究所副所長 (掛靠在加州大學洛杉磯分校），曾任美國國家基金委一個數據科學研究所輪值所長與分所長，還曾被聘為美國密蘇里科技大學冠名 Gary Havener 系主任。

他本科畢業於武漢大學計算數學專業， 碩士畢業於中國科學院（數學物理研究方向），又碩士畢業於麻薩諸塞大學阿默斯特分校，博士畢業於康奈爾大學應用數學中心（動力系統研究領域，導師菲利普・霍爾姆斯）。他隨後在加州理工學院跟隨 Stephen Wiggins 做博士後與 Instructor。

他先後在加州理工學院、克萊門森大學、加州大學洛杉磯分校和伊利諾理工學院任教。

## 科學貢獻

段金橋教授的研究領域包括隨機動力系統與非線性動力系統理論、計算和模擬，以及數學與其它學科的交叉研究 (地球與環境、生命科學等有關的隨機現象與複雜現象)。段金橋教授在非高斯隨機動力系統，隨機偏微分方程齊性化及其相關應用研究領域作出了重要貢獻， 並獲得多項科研基金和科研獎勵。

他現任 Stochastics and Dynamics  (「隨機動力系統」) 雜誌管理編輯。

他還任 Interdisciplinary Mathematical Sciences (「跨學科應用數學叢書」) 主編， 以及「Nonlinear Processes in Geophysics」編委。

## 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

## 書籍

* _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.

## 參考文獻

## 外部連結