Jianbo
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Jianbo Cui

I am an assistant professor at Department of Applied Mathematics, PolyU. Before that, I was a visiting assistant professor at School of Mathematics, Georgia Tech worked with Prof. Luca Dieci and Prof. Haomin Zhou. I did my PhD at Academy of Mathematics and Systems Science, CAS, where I was supervised by Prof. Jialin Hong.

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News

  • 04.16/2024, new preprint: Asymptotic-preserving approximations for stochastic incompressible viscous fluids and SPDEs on graph
  • 03.16/2024, our work on quantifying the effect of random dispersion for logarithmic Schrodinger equation has been accepted by SIAM/ASA Journal on Uncertainty Quantification.

  • 01.31/2024, new preprint: A supervised learning scheme for computing Hamilton-Jacobi equation via density coupling
  • 03.28/2023, the work on Stochastic Wasserstein Hamiltonian Flows has been accepted for publication in the Journal of Dynamics and Differential Equations.
  • 03.10/2023, new preprint: Energy regularized models for logarithmic SPDEs and their numerical approximations
  • 02.21/2023, the work on Optimal control for stochastic nonlinear Schrodinger equation on graph has been accepted for publication in the SIAM Journal on Control and Optimization.
  • 01.19/2023, the work on Stochastic logarithmic Schrodinger equations: energy regularized approach has been accepted for publication in the SIAM Journal on Mathematical Analysis.
  • 12.02/2022, the work on Wasserstein Hamiltonian flow with common noise on graph has been accepted by SIAM Journal on Applied Mathematics.
  • 09.13/2022,new preprint: Optimal control for stochastic nonlinear Schrodinger equation on graph
  • 08.30/2022,new preprint: Semi-implicit energy-preserving numerical schemes for stochastic wave equation via SAV approach
  • 08.25/2022, the work on Wellposedness and regularity estimate for stochastic Cahn--Hilliard equation with unbounded noise diffusion has been accepted by SPDEs: Analysis and Computations.
  • 07.09/2022, new preprint: Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation
  • 04.19/2022, the work on the continuation multiple shooting method for Wasserstein geodesic equation has been accepted by SIAM J. Sci. Comput.
  • 04.05/2022, new preprint: Wasserstein Hamiltonian flow with common noise on graph
  • 04/2022, the work on the density function of numerical approximation of Langevin equation has been accepted by Math. Comp.
  • 03/2022, one paper has been accepted by IMA J. Numer. Anal.
  • 01/2022, one paper has been accepted by Math. Comp.
  • 05/2021, I accepted the invitation to serve as a topic editor of Fractal and Fractional.
  • 10/2020, I accepted the invitation to serve as a commentator of Mathematical Reviews (No. 152664).
  • Recent Projects

    Strong and weak convergence of numerical methods for stochastic nonlinear Schoedinger equation.

    Optimal control on graph and its applications.

    Strong Convergence Rate of Numerical Approximations of SPDEs with Non-globally Lipschitz Coefficients

    Weak convergence rate and long-time behaviors of numerical approximations for SPDEs

    Recent Talks

  • 07/2024, "MS:Recent Advances in Scientific Computing and Learning" in the International Conference on Scientific Computation and Differential Equations 2024, Singapore
  • 04/2024, Modern Methods for Differential Equations of Quantum Mechanics, the Banff International Research Station for Mathematical Innovation and Discovery (BIRS), Canada
  • 12/2023, Workshop on Graph Theory, Optimization and Scientific Computing, The Hong Kong Polytechnic University
  • 12/2023, The One World Stochastic Numerics and Inverse Problems seminar (online)
  • 12/2023, Ninth Youth Symposium on Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing, China
  • 11/2023, 2023 Workshop on stochastic computations, Southern University of Science and Technology, Shenzhen, China
  • 11/2023, Workshop on Stochastic Dynamical Systems and Machine Learning, Xiamen University and Tianyuan Mathematical Center in Southeast China, Xiamen, China
  • 10/2023, 2023 Workshop on Theory, Algorithms and Related Issues in Dynamical Systems, Nanjing University, Nanjing, China
  • 08/2023, The First Workshop on Analysis and Computing at MSU-BIT University, Shenzhen MSU-BIT University, Shenzhen, China
  • 06/2023, 2023 Youth Workshop on Theory and Algorithms of Stochastic Dynamical Systems, National University of Defense Technology, Changsha, China
  • 04/2023, 2023 Frontiers Symposium on Numerical Computation of Stochastic Differential Equations, Tiangong University, Tianjing, China
  • 03/2023, Seminar on computation mathematics, Southeast University, Jiangsu, China (online)
  • 09/2022, 2022 Frontier Seminar on Numerical Methods, Sichuan University, Sichuan, China (online)
  • 08/2022, Lecture on "optimal transport on graph and its application", Chinese Academy of Sciences, Beijing, China (online)
  • 04/2021, Seminar on Stochastic Partial Differential Equations Perserving Structure Algorithms for Youth Scholars, Chinese Academy of Sciences, Beijing, China (online)
  • 02/2021, 2021 Georgia Scientific Computing Symposium (GSCS), University of Georgia, Atlanta, USA (online)
  • 12/2020, Central South University, School of Mathematics and Statistics, Changsha, China (online)
  • 02/2020, 2020 Georgia Scientific Computing Symposium (GSCS), Emory University, Atlanta, USA
  • 02/2020, Applied and Computational Mathematics Seminar, Georgia Institute of Technology, Atlanta, USA
  • 11/2018, Forum on Numerical Analysis for SDEs and SPDEs, Chinese Academy of Sciences, Beijing, China
  • 10/2018, International Conference on Stochastic Partial Differential Equations, University of Alberta, Edmonton, Canada
  • 09/2018, The 1st Peking University Top Doctoral Seminar on Computing and Applied Mathematics and the 4th Beijing Computational Mathematics Graduate Forum, Peking University, Beijing, China
  • 09/2018, Numerical Analysis of Stochastic Partial Differential Equations, University of Gothenburg, Gothenburg, Sweden
  • 06/2018, Seminar on Hot Topics in Stochastic Computing, Tianyuan Mathematical Center in Northeast China, Changchun, China
  • 06/2018, The 40th Stochastic Processes and Their Applications Conference, Gothenburg, Sweden
  • 11/2017, Forum on Numerical Analysis for SDEs and SPDEs, AMSS, CAS, Beijing, China
  • 10/2017, Efficient Numerical Methods for Stochastic Hamiltonian Partial Differential Equations, Central South University, Changsha, China
  • 09/2017, SciCADE 2017, International Conference on Scientific Computation and Differential Equations, University of Bath, Bath
  • 05/2017, Workshop on Dynamical System and Its Applications, Dalian University of Technology, Dalian, China
  • 01/2017, 10th International Conference on Computational Physics, University of Macau, Macau, China
  • 11/2016, 20th IMACS World Congress, Xiamen University, Xiamen, China
  • Teaching

  • Semester 2 2023/2024, AMA 3201, Computational Methods
  • Semester 2 2023/2024, AMA 10071, Calculus and Linear Algebra
  • Semester 1 2023/2024, AMA 3724, Further Mathematical Methods
  • Semester 2 2022/2023, AMA 3201, Computational Methods
  • Semester 2 2022/2023, AMA 10071, Calculus and Linear Algebra
  • Semester 1 2022/2023, AMA 2703, Mathematical Methods for Finance
  • Semester 2 2021/2022, AMA 10071, Calculus and Linear Algebra
  • Spring 2021, Math 1554G, Linear Algebra
  • Fall 2020, Math 1553B, Introduction to Linear Algebra
  • Spring 2020, Math 1553B, Introduction to Linear Algebra
  • Fall 2019, Math 1553E, Introduction to Linear Algebra
  • Research

    My current research interests include numerical analysis, stochastic ODEs and PDEs, optimal transport, optimal control, structure-preserving algorithms, Hamiltonian systems, dynamical systems, ergodic theory, etc.

    Publications

    1. Cui, J.; Sun, L. Quantifying the effect of random dispersion for logarithmic Schrodinger equation to appear in SIAM/ASA Journal on Uncertainty Quantification.

    2. Cui, J.; Sun, L. Stochastic logarithmic Schrodinger equations: energy regularized approach SIAM J. Math. Anal. 55 (2023), no. 4, 3044-3080.

    3. Cui, J.; Liu, S.; Zhou, H. Optimal control for stochastic nonlinear Schrodinger equation on graph SIAM J. Control Optim. 61 (2023), no. 4, 2021-2042.

    4. Cui, J.; Liu, S.; Zhou, H. Stochastic Wasserstein Hamiltonian Flows J. Dyn. Diff. Equat. (2023), https://doi.org/10.1007/s10884-023-10264-4

    5. Cui, J.; Hong, J. Wellposedness and regularity estimate for stochastic Cahn--Hilliard equation with unbounded noise diffusion Stoch. Partial Differ. Equ. Anal. Comput. 11 (2023), no. 4, 1635-1671

    6. Cui, J.; Liu, S.; Zhou, H. Wasserstein Hamiltonian flow with common noise on graph SIAM J. Appl. Math. 83 (2023), no. 2, 484-509

    7. Chen, C. ; Cui, J.; Hong, J.; Sheng, D. Accelerated Exponential Euler Scheme for Stochastic Heat Equation: Convergence rate of Densities. IMA J. Numer. Anal. 43 (2023), no. 2, 1181-1220.

    8. Cui, J.; Dieci, L.; Zhou, H. A continuation multiple shooting method for Wasserstein geodesic equation SIAM J. Sci. Comput. 44 (2022), no. 5, A2918-A2943. GitHub

    9. Cui, J.; Hong, J.; Sheng, D. Density function of numerical solution of splitting AVF scheme for stochastic Langevin equation. . Math. Comp. 91 (2022), no. 337, 2283-2333.

    10. Cui, J.; Dieci, L.; Zhou, H. Time Discretizations of Wasserstein-Hamiltonian Flows. Math. Comp. 91 (2022), no. 335, 1019-1075.

    11. Cui, J.; Hong, J.; Sun, L. Strong convergence of full discretization for stochastic Cahn-Hilliard equation driven by additive noise. SIAM J. Numer. Anal. 59 (2021), no. 6, 2866-2899.

    12. Cui, J.; Liu S.; Zhou, H. What is a stochastic Hamiltonian process on finite graph? An optimal transport answer. J. Differential Equations 305 (2021), 428-457.

    13. Cui, J.; Hong, J.; Sun, L. Weak convergence and invariant measure of a full discretization for parabolic SPDEs with non-globally Lipschitz coefficients. Stochastic Process. Appl. 134 (2021), 55-93.

    14. Cui, J.; Hong, J. Absolute continuity and numerical approximation of stochastic Cahn-Hilliard equation with unbounded noise diffusion. J. Differential Equations 269 (2020), no. 11, 10143-0180.

    15. Cohen, D.; Cui, J.; Hong, J.; Sun, L. Exponential integrators for stochastic Maxwell's equations driven by Ito noise. J. Comput. Phys. 410 (2020), 109382, 21 pp.

    16. Cui, J.; Hong, J.; Sun, L. On global existence and blow-up for damped stochastic nonlinear Schrodinger equation. Discrete Contin. Dyn. Syst. Ser. B 24 (2019), no. 12, 6837-6854.

    17. Brehier, C. E.; Cui, J.; Hong, J. Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen-Cahn equation. IMA J. Numer. Anal. 39 (2019), no. 4, 2096-2134.

    18. Cui, J.; Hong, J. Strong and weak convergence rates of a spatial approximation for stochastic partial differential equation with one-sided Lipschitz coefficient. SIAM J. Numer. Anal. 57 (2019), no. 4, 1815-1841.

    19. Cui, J.; Hong, J.; Liu, Z.; Zhou, W. Strong convergence rate of splitting schemes for stochastic nonlinear Schrodinger equations. J. Differential Equations 266 (2019), no. 9, 5625-5663.

    20. Cui, J.; Hong, J. Analysis of a splitting scheme for damped stochastic nonlinear Schrodinger equation with multiplicative noise. SIAM J. Numer. Anal. 56 (2018), no. 4, 2045-2069.

    21. Niu, X.; Cui, J.; Hong, J.; Liu, Z. Explicit pseudo-symplectic methods for stochastic Hamiltonian systems. BIT 58 (2018), no. 1, 163-178.

    22. Cui, J.; Hong, J.; Liu, Z. Strong convergence rate of finite difference approximations for stochastic cubic Schrodinger equations. J. Differential Equations 263 (2017), no. 7, 3687-3713.

    23. Cui, J.; Hong, J.; Liu, Z.; Zhou, W. Stochastic symplectic and multi-symplectic methods for nonlinear Schrodinger equation with white noise dispersion. J. Comput. Phys. 342 (2017), 267-285.

    24. Cui, J.; Liu, Z.; Miao, L.; Wang, X. Holder continuity for parabolic Anderson equation with non-Gaussian noise. J. Math. Anal. Appl. 441 (2016), no. 2, 684-691.

    Preprints:

    1. Cui, J.; Sheng, D. Asymptotic-preserving approximations for stochastic incompressible viscous fluids and SPDEs on graph arXiv:2404.09168

    2. Cui, J.; Liu, S.; Zhou, H. A supervised learning scheme for computing Hamilton-Jacobi equation via density coupling arXiv:2401.1595

    3. Cui, J.; Sun, L. Weak approximation for stochastic reaction-diffusion equation near sharp interface limit arXiv:2307.08241

    4. Cui, J. Regularization effect of noise on fully discrete approximation for stochastic reaction-diffusion equation near sharp interface limit arXiv:2307.08246

    5. Cui, J.; Hou, D.; Qiao, Z. Energy regularized models for logarithmic SPDEs and their numerical approximations arXiv:2303.05003

    6. Cui, J.; Hong, J.; Sun, L. Semi-implicit energy-preserving numerical schemes for stochastic wave equation via SAV approach arXiv2208.13394

    7. Brehier, C. E.; Cui, J.; Wang, X. Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation arXiv:2207.09266

    8. Cui, J. Explicit Numerical Methods for High Dimensional Stochastic Nonlinear Schrodinger Equation: Divergence, Regularity and Convergence arXiv:2112.10177

    9. Cui, J.; Hong, J.; Sun, L. Structure-preserving splitting methods for stochastic logarithmic Schrodinger equation via regularized energy approximation arXiv:2111.04402

    10. Cui, J.; Hong, J.; Ji, L.; Sun, L. Energy-preserving exponential integrable numerical method for stochastic cubic wave equation with additive noise arXiv:1909.00575

    Research Group

    PhD students:

  • Qujiangxue Chen, working on optimal transport and its numerical algorithm
  • Postdoc fellows:

  • Dr. Derui Sheng (CAS), Joined in 05/2023
  • Dr. Tao Zhou (CAS), Joined in 08/2023
  • Dr. Chenhui Zhang (Taiyuan University of Technology), Joined in 12/2023
  • Open Positions

  • Several PhD student positions are available in the research group of Dr. Jianbo Cui.
    Candidates with Bachelor degree in mathematics or computer science are welcome to apply.

    Application procedure: send a CV and transcript to email address: jianbo.cui@polyu.edu.hk

    To find out more information about the PhD program in our department, please visit
  • Several postdoc positions are available in the research group of Dr. Jianbo Cui.
    The term of appointment will be one or two year with the possibility of one additional years contingent upon satisfactory performance. The term of appointment may commence anytime.

    Responsibilities and qualifications:

    You will be part of a team with expertise in many areas of numerical analysis, stochastic analysis and scientific computing. You will contribute to developing mathematical theory and computational methods for solving scientific problems including optimal transport, stochastic control and stochastic partial differential equations. Current research topics within the team include (but not limited to):

    Analysis of partial differential equations (e.g., PDEs on graph, SPDEs);

    Analysis of long-time behaviors of dynamical systems (e.g., limit theorem, invariant measure);

    Structure-preserving numerical method (e.g., OT problem, density approximation);

    Machine learning for solving PDEs and SDEs.

    Candidates must have obtained a PhD degree in mathematics, applied mathematics, computer science, statistics, or related fields, and have a strong background and track record of accomplishment in numerical analysis, stochastic analysis, optimal control and machine learning. A strong background in analysis (real analysis, functional analysis, PDEs) or outstanding programming skills (e.g., MATLAB, Python) is highly desirable.

    Application procedure: send a CV and transcript to email address: jianbo.cui@polyu.edu.hk

  • Services

  • Local Organizer of Workshop on Graph Theory, Optimization and Scientific Computing (Organizing Committe consists of Prof. Yanping Lin, Prof. Zhonghua Qiao, Prof. Guiying Yan)

  • Local Organizer and General Enquiry of The Seventh International Conference on Scientific Computing and Partial Differential Equations (SCPDE23) (Organizing Committe consists of Prof. Zhonghua Qiao, Prof. Chi-Wang Shu, Prof. Tao Tang, Prof. Tong Yang)

  • Organizer of Minisymposia [00886] Numerical methods for stochastic partial differential equations in 10th International Congress in industry and Applied Mathematics (ICIAM 2023 TOKYO) (With Prof. Charles-Edouard Brehier)

  • 2022 to present | Assistant Programme Leader of MSc in Operational Research and Risk Analysis

  • 2023 to present | Reviewer of zbMath Open (ID 20464)

  • 2021 to present | Journal Topical Advisory Panel of Fractal and Fractional

  • 2020 to present | Commentator of Mathematical Reviews (No. 152664)

  • Journal Reviewers:

    SIAM Journal on Numerical Analysis;

    Numerische Mathematik;

    Mathematics of Computation;

    SIAM Review;

    Annals of Applied Probability;

    Stochastic Process. Appl.;

    Journal of Differential Equations;

    IMA Journal of Numerical Analysis;

    SIAM Journal on Control and Optimization;

    SPDEs: Analysis and Computations;

    Communications in Mathematical Sciences;

    Applied Numerical Mathematics;

    Journal of Computational Mathematics;

    Zeitschrift fur angewandte Mathematik und Physik;

    Discrete and Continuous Dynamical Systems Series S;

    Acta Mathematica Scientia;

    Computers and Mathematics with Applications;

    Communications on Pure and Applied Analysis;

    International Journal of Numerical Analysis and Modeling;

    CSIAM Transactions on Applied Mathematics;

    J. Integral Equations Appl.; Results Appl. Math.;

    Advances in Applied Mathematics and Mechanics;

    Journal of Theoretical Probability;

    AIMS Mathematics;
    ... etc.

  • Awards

  • 2018, National scholarship, Chinese Academy of Sciences

  • 2018, President Award, Chinese Academy of Sciences

  • 2018, Pacemaker to Merit Student, Chinese Academy of Sciences

  • 2013, National Encouragement Scholarship, Sichuan University

  • My Office: TU727, Yip Kit Chuen Bldg.

    My Phone Number: +852 2766 6956