本人主要从事最优控制及应用、非线性分析、偏微分方程、动力系统,以及人工智能相关问题的研究。相关科研成果在《IEEE Transactions on Automatic Control》、《Journal of Differential Equations》、《Nonlinearity》、《Discrete and Continuous Dynamical Systems》、《Journal of Mathematical Physics》等国内外学术期刊上发表。
已发表论文
1. Guoyuan Chen. Deep neural network approximations for the stable manifolds of the Hamilton-Jacobi-Bellman equations. IEEE Transactions on Automatic Control, Vol. 69, No. 10, 7239-7246, 2024. DOI: 10.1109/TAC.2024.3396107.
2. Guoyuan Chen, Gaosheng Zhu, Symplectic algorithms for stable manifolds in control theory, IEEE Transactions on Automatic Control, Vol. 67, No. 6, 3105-3111, 2022.
3. Yi Wang, Zhongjun Ma, Guoyuan Chen (通讯), Jinde Cao, Design of consensus and cluster consensus controller for first-order nonlinear multi-agent systems based on subgroup structure, Neurocomputing 600, 128141, 2024.
4. Yi Wang, Haiyu Song, Guoyuan Chen, Zhongjun Ma, Jinde Cao, Components of Cluster-Lag Consensus for Second-Order Multiagent Systems With Adaptive Controller on Cooperative–Competitive Networks, IEEE Transactions on Cybernetic, Vol. 53, No. 5, 2852-2863, 2023.
5. Guoyuan Chen. Nondegeneracy of Ground States and Multiple Semiclassical Solutions of the Hartree Equation for General Dimensions. Results in Math, 76, 34, 2021.
6. 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.
7. 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.
8. Guoyuan Chen, Youquan Zheng, Fractional nonlinear Schr\"odinger equations with singular potential in $\mathbf R^n$, Journal of Mathematical Physics, 59, 071507, 2018.
9. Guoyuan Chen, Singularly perturbed Neumann problem for fractional Schrödinger equations, SCIENCE CHINA-Mathematics, Vol. 61(4), 695-708, 2018.
10. Guoyuan Chen, Multiple semiclassical standing waves for fractional nonlinear Schrödinger equations, Nonlinearity, Vol. 28(4), 927-949, 2015.
11. 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.
12. Guoyuan Chen, Youquan Zheng, Concentration phenomenon for fractional nonlinear Schrödinger equations, Communications on Pure and Applied Analysis, Vol. 13, 2359-2376, 2014.
13. Guoyuan Chen, Youquan Zheng, Stationary solutions of non-autonomous Maxwell–Dirac systems, Journal of Differential Equations, Vol. 255, 840-864, 2013.
14. Guoyuan Chen, Fredholm index and spectral flow in non-self-adjoint case, Acta Mathematica Sinica, English Series, Vol. 29, 957-992, 2013.
15. Guoyuan Chen, Youquan Zheng, Solitary waves for the Klein–Gordon–Dirac model, Journal of Differential Equations, Vol. 253, 2263-2284, 2012.
16. 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.