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姓名:陈国元

陈国元博士,现任浙江财经大学数据科学学院副教授硕士生导师。主要研究领域为非线性分析,偏微分方程,动力系统,控制论,及相关的人工智能交叉应用

教育与工作经历:

20127月至今,浙江财经大学任教。

20089月-20127月,南开大学陈省身数学研究所基础数学专业学习,获博士学位。

20059月-20087月,南开大学陈省身数学研究所基础数学专业学习,获硕士学位。

20019月-20057,河北工业大学数学与应用数学专业学习,获学士学位。

20177月-20187,加拿大英属哥伦比亚大学数学专业,访问学者。

  • 主要科研项目:

  1. 一般阶非线性椭圆方程中若干问题的研究(No.11401521),国家自然科学基金青年基金,2015.01-2017.12,主持。

  2. 含有分数阶算子的非线性椭圆方程半经典解的研究(No. LY18A010023),浙江省自然科学基金一般项目,2018.01-2020.12,主持。

  3. 关于Schrödinger 方程解的集中性的研究(No. LQ13A010003),浙江省自然科学基金青年基金,2013.01-2015.12,主持。

  • 科研概述

本人主要研究非线性分析,偏微分方程,Hamilton系统,最优控制及人工智能的相关问题。具体如下:Hamilton-Jacobi方程(一阶非线性偏微分方程)及其特征Hamilton系统的分析,解的正则性,数值计算及其在最优控制、人工智能中的应用;一般阶非线性椭圆方程和抛物方程的集中解,爆破解,及解的多重性,正则性等问题;一般椭圆型拟微分算子的分析。

相关研究成果在《IEEE Transactions on Automatic Control》、《Journal of Differential Equations》、《Nonlinearity》、《Discrete and Continuous Dynamical Systems》、Journal of Mathematical Physics》、《SCIENCE CHINA Mathematics》等国内外权威学术期刊上发表。

  • 论文、著作

  1. Guoyuan Chen, Xing Lin, Optimal feedback control for asymptotic stabilization of the inverted 3D pendulum based on deep neural networks, preprinted, 2021.

  2. Guoyuan Chen, Deep neural network approximations for the stable manifolds of the Hamilton-Jacobi-Bellman equations, arXiv:2020.15350. 2020.

  3. Guoyuan Chen, Gaosheng Zhu, Symplectic algorithms for stable manifolds in control theory, IEEE Transactions on Automatic Control, Vol. 67, No. 6, 3105-3111, DOI: 10.1109/TAC.2021.3093594, 2022.

  4. Guoyuan Chen. Nondegeneracy of Ground States and Multiple Semiclassical Solutions of the Hartree Equation for General Dimensions. Results in Math, 76, 34, 2021.

  5. Guoyuan Chen, Yong Liu, Juncheng Wei, Nondegeneracy of harmonic maps R2 to S2, Discrete and Continuous Dynamical Systems A, Volume 40, Number 6, June 2020, pp. 3215-3233. doi:10.3934/dcds.2019228.

  6. Guoyuan Chen, Juncheng Wei, Yifu Zhou, Finite time blow-up for the fractional critical heat equation in Rn, Nonlinear Analysis: Theory, Methods and Applications, 193, 111420, April 2020.

  7. Guoyuan Chen, Youquan Zheng, Fractional nonlinear Schr\"odinger equations with singular potential in $\mathbf R^n$, Journal of Mathematical Physics, 59, 071507, 2018.

  8. Guoyuan Chen, Singularly perturbed Neumann problem for fractional Schrödinger equations, SCIENCE CHINA Mathematics, Vol. 61(4), 695-708, 2018.

  9. Guoyuan Chen, Multiple semiclassical standing waves for fractional nonlinear Schrödinger equations, Nonlinearity, Vol. 28(4), 927-949, 2015.

  10. Guoyuan Chen, Youquan Zheng, A perturbation result for the Q_{\gamma} curvature on S^n, Nonlinear Analysis: Theory, Methods and Applications, Vol. 97, 4-14, 2014.

  11. Guoyuan Chen, Youquan Zheng, Concentration phenomenon for fractional nonlinear Schrödinger equations, Communications on Pure and Applied Analysis, Vol. 13, 2359-2376, 2014.

  12. Guoyuan Chen, Youquan Zheng, Stationary solutions of non-autonomous Maxwell–Dirac systems, Journal of Differential Equations, Vol. 255, 840-864, 2013.

  13. Guoyuan Chen, Fredholm index and spectral flow in non-self-adjoint case, Acta Mathematica Sinica, English Series, Vol. 29, 957-992, 2013.

  14. Guoyuan Chen, Youquan Zheng, Solitary waves for the Klein–Gordon–Dirac model, Journal of Differential Equations, Vol. 253, 2263-2284, 2012.

  15. Bernhelm Booss-Bavnbek, Guoyuan Chen, Matthias Lesch, Chaofeng Zhu, Perturbation of sectorial projections of elliptic pseudo-differential operators, Journal of Pseudo-differential Operators and Applications, Vol. 1 (3), 49-79, 2012.

     


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