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.
Email / Google Scholar / AMS / ORCiD
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
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.
Cui, J.; Sun, L. Stochastic logarithmic Schrodinger equations: energy regularized approach SIAM J. Math. Anal. 55 (2023), no. 4, 3044-3080.
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.
Cui, J.; Liu, S.; Zhou, H. Stochastic Wasserstein Hamiltonian Flows J. Dyn. Diff. Equat. (2023), https://doi.org/10.1007/s10884-023-10264-4
Cui, J.; Hong, J. Wellposedness and regularity estimate for stochastic Cahn--Hilliard equation with unbounded noise diffusion SPDEs: Analysis and Computations., https://doi.org/10.1007/s40072-022-00272-8
Cui, J.; Liu, S.; Zhou, H. Wasserstein Hamiltonian flow with common noise on graph SIAM J. Appl. Math. 83 (2023), no. 2, 484-509
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.
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
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.
Cui, J.; Dieci, L.; Zhou, H. Time Discretizations of Wasserstein-Hamiltonian Flows. Math. Comp. 91 (2022), no. 335, 1019-1075.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Niu, X.; Cui, J.; Hong, J.; Liu, Z. Explicit pseudo-symplectic methods for stochastic Hamiltonian systems. BIT 58 (2018), no. 1, 163-178.
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.
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.
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.
Cui, J.; Liu, S.; Zhou, H. A supervised learning scheme for computing Hamilton-Jacobi equation via density coupling arXiv:2401.1595
Cui, J.; Sun, L. Weak approximation for stochastic reaction-diffusion equation near sharp interface limit arXiv:2307.08241
Cui, J. Regularization effect of noise on fully discrete approximation for stochastic reaction-diffusion equation near sharp interface limit arXiv:2307.08246
Cui, J.; Sun, L. Quantifying the effect of random dispersion for logarithmic Schrodinger equation arXiv:2306.06617
Cui, J.; Hou, D.; Qiao, Z. Energy regularized models for logarithmic SPDEs and their numerical approximations arXiv:2303.05003
Cui, J.; Hong, J.; Sun, L. Semi-implicit energy-preserving numerical schemes for stochastic wave equation via SAV approach arXiv2208.13394
Brehier, C. E.; Cui, J.; Wang, X. Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation arXiv:2207.09266
Cui, J. Explicit Numerical Methods for High Dimensional Stochastic Nonlinear Schrodinger Equation: Divergence, Regularity and Convergence arXiv:2112.10177
Cui, J.; Hong, J.; Sun, L. Structure-preserving splitting methods for stochastic logarithmic Schrodinger equation via regularized energy approximation arXiv:2111.04402
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
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 SIAM Journal on Numerical Analysis;
Numerische Mathematik;
Mathematics of Computation;
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.