Li, Lei

Institute of Natural Sciences; School of mathematical sciences.
Shanghai Jiao Tong University

Office: 323 Science Building No. 5
E-mail: leili2010 AT sjtu DOT edu DOT cn

Here is my CV.


I'm a tenure track Associate Professor at Shanghai Jiao Tong University. My interest lies in applied math, including


Tenure track Associate Professor, SJTU; 2018-present

Assistant Research Professor, Duke University, 2015-2018


2010-2015. Mathematics. Phd. UW-Madison.

2013. Mathematics. MA. UW-Madison

2012. Computer Science. MS. UW-Madison.

2006-2010. Mathematics and Physics. BS. Tsinghua University, Beijing.


Numerical stability of Gr\"unwald-Letnikov method for time fractional delay differential equations
L. Li, D. Wang
Random Batch Methods for classical and quantum interacting particle systems and statistical samplings
S. Jin, L. Li
On the Random Batch Method for second order interacting particle systems
S. Jin, L. Li, Y. Sun
Energy and quadratic invariants preserving methods for Hamiltonian systems with holonomic constraints
L. Li, D. Wang
A direct simulation approach for the Poisson-Boltzmann equation using the Random Batch Method
L. Li, J. Liu, Y. Tang
On Runge-Kutta methods for the water wave equation and its simplified nonlocal hyperbolic model
L. Li, J. Liu, Z. Liu, Y. Yang, Z. Zhou


  1. A random batch Ewald method for particle systems with Coulomb interactions
    S. Jin, L. Li, Z. Xu, Y. Zhao SIAM J. Sci. Comput. Accepted
  2. Scheduling fixed length quarantines to minimize the total number of fatalities during an epidemic
    Y. Feng, G. Iyer, L. Li. J. Math. Biology Accepted
  3. Numerical methods for stochastic differential equations based on Gaussian mixture
    L. Li, J. Lu, J. Mattingly, L. Wang. Comm. Math. Sci.Accepted
  4. Complete Monotonicity-preserving numerical methods for time fractional ODEs
    L. Li, D. Wang Comm. Math. Sci. Accepted
  5. On the mean field limit of Random Batch Method for interacting particle systems
    S. Jin, L. Li. Science China Mathematics Accepted pdf file
  6. Convergence of Random Batch Method for interacting particles with disparate species and weights
    S. Jin, L. Li, J. Liu SIAM J. Numer. Anal. 2021. Vol. 59, Issue 2, 746--768
  7. A consensus-based global optimization method for high dimensional machine learning problems
    J. A. Carrillo, S. Jin, L. Li, Y. Zhu ESAIM: Control, Optimisation and Calculus of Variations 2021. Vol. 27, S5 pdf file
  8. Large time behaviors of upwind schemes and B-schemes for Fokker-Planck equations on R by jump processes
    L. Li, J. Liu Math. Comp. 2020. Vol. 89, No. 235, 2283--2320 pdf file
  9. A stochastic version of Stein Variational Gradient Descent for efficient sampling
    L. Li, Y. Li, J. Liu, Z. Liu, J. Lu Commun. Appl. Math. Comput. Sci.(CAMCoS) 2020. Vol. 15, Issue 1, 37--63
  10. A random-batch Monte Carlo method for many-body systems with singular kernels
    L. Li, Z. Xu, Y. Zhao SIAM J. Sci. Comput. 2020. Vol. 42, No. 3, A1486-A1509 pdf file
  11. Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation
    Y. Feng, T. Gao, L. Li, J. Liu, Y. Lu Comm. Math. Sci. 2020. Vol. 18, Issue 1 pdf file
  12. Numerical approximation and fast evaluation of the overdamped generalized Langevin equation with fractional noise
    D. Fang, L. Li ESAIM: Math. Model. Numer. Anal. 2020. Vol. 54, No. 2, 431-463 pdf file
  13. On the mean field limit for Brownian particles with Coulomb interaction in 3D
    L. Li, J. Liu, P. Yu J. Math. Phys. 2019. Vol. 60. 111501 pdf file
  14. Random batch methods (RBM) for interacting particle systems
    S. Jin, L. Li, J. Liu J. Comput. Phys. 2020. Vol. 400, No. 1 pdf file
  15. A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows
    L. Li, J. Liu SIAM J. Numer. Anal. 2019. Vol. 57, No. 5, 2095-2120 pdf file
  16. Patched peakon weak solutions of the modified Camassa-Holm equation
    Y. Gao, L. Li, J. Liu Physica D: Nonlinear Phenomena 2019. Vol. 390. 15-35 pdf file
  17. On the diffusion approximation of nonconvex stochastic gradient descent
    W. Hu, C. J. Li, L. Li, J. Liu Annals of Mathematical Sciences and Applications 2019. Vol. 4, No. 1, 3-32 pdf file
  18. Semi-groups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations
    Y. Feng, L. Li, J. Liu Comm. Math. Sci. 2018. Vol. 16, No. 3 pdf file
  19. Some compactness criteria for weak solutions of time fractional PDEs
    L. Li, J. Liu SIAM: Math. Anal. 2018. Vol. 50, Issue 4. 3963-3995 pdf file
  20. A generalized definition of Caputo derivatives and its application to fractional ODEs
    L. Li, J. Liu SIAM: J. Math. Anal. 2018. Vol. 50, Issue 3. 2867-2900pdf file
  21. A dispersive regularization for the modified Camassa-Holm equation
    Y. Gao, L. Li, J. Liu SIAM J. Math. Anal. 2018. Vol. 50, Issue 3. 2807-2838pdf file
  22. Cauchy problems for Keller-Segel type time-space fractional diffusion equation
    L. Li, J. Liu, L. Wang J. Differ. Equations 2018. Vol. 265, Issue 3 pdf file
  23. A note on one-dimensional time fractional ODEs
    Y. Feng, L. Li, J. Liu, X. Xu Applied Mathematics Letters 2018. Vol. 83. pdf file
  24. Continuous and discrete one dimensional autonomous fractional ODEs
    Y. Feng, L. Li, J. Liu, X. Xu Discrete and Continuous Dynamical Systems- Series B 2018. Vol. 23, Issue 8 pdf file
  25. p-Euler equations and p-Navier-Stokes equations
    L. Li, J. Liu J. Differ. Equations 2018. Volume 264, Issue 7 pdf file
  26. A note on deconvolution with completely monotone sequences and discrete fractional calculus
    L. Li, J. Liu Quart. Appl. Math. 2018. Vol. 76, Issue 1 pdf file
  27. Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
    L. Li, J. Liu, J. Lu J. Stat. Phys. 2017. Vol. 169, Issue 2.pdf file
  28. A locally gradient preserving reinitialization for level set functions
    L. Li, X. Xu, S. E. Spagnolie Journal of Scientific Computing. 2017. Vol. 71, Issue 1. pdf file
  29. Swimming and pumping by helical waves in viscous and viscoelastic fluids
    L. Li, S. E. Spagnolie Physics of fluids. 2015. Vol. 27, Issue 2.pdf file
  30. Analytical solution for laterally loaded long piles basedon Fourier-Laplace integral
    F. Liang, Y. Li, L. Li, J. Wang. Applied Mathematical Modelling. 2014. Vol. 38. Issue 21 pdf file
  31. The instability of a sedimenting suspension of weakly flexible fibres
    H. Manikantan, L. Li, S. E. Spagnolie, D. Saintillan. Journal of fluid mechanics. 2014. Vol 756. 935-964pdf file
  32. Swimming and pumping of rigid helical bodies in viscous fluids
    L. Li, S. E. Spagnolie, Physics of fluids. 2014. Vol. 26, Issue 4.pdf file
  33. The sedimentation of flexible filaments
    L. Li, H. Manikantan, D. Saintillan, S. E. Spagnolie. Journal of fluid mechanics. 2013. Vol 735. 705-736pdf file


Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
2015. UW-Madison.