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

Accepting Postdocs Salary can be raised to a satisfactory level. Email to discuss. Those who are familiar with analysis and/or probability are more preferred.


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

Here is my CV.


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.


Study seminar on many-body systems


Propagation of chaos in path spaces via information theory
L. Li, Y. Wang, Y. Wang
Some Gr\"onwall inequalities for a class of discretizations of time fractional equations on nonuniform meshes
Y. Feng, L. Li, J. Liu, T. Tang
Solving stationary nonlinear Fokker-Planck equations via sampling
L. Li, Y. Tang, J. Zhang
A class of monotonicity-preserving variable-step discretizations for Volterra integral equations
Y. Feng, L. Li
Geometric ergodicity of SGLD via reflection coupling
L. Li, J.-G. Liu, Y. Wang
A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamics
L. Li, Y. Wang
Fluctuation suppression and enhancement in interacting particle systems
J. Chen and L. Li


  1. On the completely positive kernels for nonuniform meshes
    F. Feng, L. Li Quarterly of Applied Mathematics Accepted
  2. On uniform-in-time diffusion approximation for stochastic gradient descent
    L. Li, Y. Wang Methods and Applications of Analysis Accepted
  3. Convergence analysis of an explicit method and its random batch approximation for the McKean-Vlasov equations with non-globally Lipschitz conditions
    Q. Guo, J. He, L. Li ESAIM: M2AN Accepted
  4. On the convergence of continuous and discrete unbalanced optimal transport models
    Z. Xiong, L. Li, Y.-N. Zhu, X. Zhang SIAM J. Numer. Anal. 2024, Vol. 62, Iss. 2 pdf file
  5. Existence of weak solutions to p-Navier-Stokes equations
    Y. Feng, L. Li, J. Liu, X. Xu DCDS-B 2024, Vol. 29, No. 4 pdf file
  6. A machine learning framework for geodesics under spherical Wasserstein-Fisher-Rao metric and its application for weighted sample generation
    Y. Jing, J. Chen, L. Li, J. Lu Journal of Scientific Computing 2024, Vol. 98, No. 5 pdf file
  7. Ergodicity and long-time behavior of the Random Batch Method for interacting particle systems
    S. Jin, L. Li, X. Ye and Z. Zhou Mathematical Models and Methods in Applied Sciences 2023, Vol. 33, No. 1 pdf file
  8. Energy and quadratic invariants preserving methods for Hamiltonian systems with holonomic constraints
    L. Li, D. Wang J. Comput. Math. 2023, Vol. 41, No. 1 pdf file
  9. A splitting Hamiltonian Monte Carlo method for efficient sampling
    L. Li, L. Liu, Y. Peng CSIAM Tran. Appl. Math. 2023, Vol. 4, Number 1. pdf file
  10. A random batch Ewald method for charged particles in the isothermal-isobaric ensemble
    J. Liang, P. Tan, L. Hong, S. Jin, Z. Xu, L. Li J. Chem. Phys. 2022,157,144102 pdf file
  11. On Energy Stable Runge-Kutta Methods for the Water Wave Equation and Its Simplified Non-Local Hyperbolic Model
    L. Li, J. Liu, Z. Liu, Y. Yang, Z. Zhou Communications in Computational Physics 2022, Vol. 32, Issue 1. pdf file
  12. Some random batch particle methods for the Poisson-Nernst-Planck and Poisson-Boltzmann equations
    L. Li, J. Liu, Y. Tang Communications in Computational Physics 2022, Vol. 32, Issue 1. pdf file
  13. On the Random Batch Method for second order interacting particle systems
    S. Jin, L. Li, Y. Sun (SIAM) Multiscale Modeling and Simulation 2022, Vol. 20, Issue 2 pdf file
  14. Numerical stability of Gr\"unwald-Letnikov method for time fractional delay differential equations
    L. Li, D. Wang BIT Numerical Mathematics 2022. Vol. 62, Issue 3, 995--1027. pdf file
  15. On the mean field limit of Random Batch Method for interacting particle systems
    S. Jin, L. Li. Science China Mathematics 2022. Vol. 65, Issue 1.pdf file
  16. Superscalability of the random batch Ewald method
    J. Liang, P. Tan, Y. Zhao, L. Li, S., Jin, L. Hong, Z. Xu J. Chem. Phys. 156, 014114 (2022). pdf file
  17. Scheduling fixed length quarantines to minimize the total number of fatalities during an epidemic
    Y. Feng, G. Iyer, L. Li. J. Math. Biology 2021. 82(69), 1-17pdf file
  18. A random batch Ewald method for particle systems with Coulomb interactions
    S. Jin, L. Li, Z. Xu, Y. Zhao SIAM J. Sci. Comput. 2021. 43(4),B937-B960. pdf file
  19. Numerical methods for stochastic differential equations based on Gaussian mixture
    L. Li, J. Lu, J. Mattingly, L. Wang. Comm. Math. Sci.2021. Vol. 19, No. 6 pdf file
  20. Complete Monotonicity-preserving numerical methods for time fractional ODEs
    L. Li, D. Wang Comm. Math. Sci. 2021. Vol. 19, No. 5, pp. 1301-1336 pdf file
  21. 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.pdf file
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. Random batch methods (RBM) for interacting particle systems
    S. Jin, L. Li, J. Liu J. Comput. Phys. 2020. Vol. 400, No. 1 pdf file
  29. 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
  30. 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
  31. 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
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. 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
  38. A note on one-dimensional time fractional ODEs
    Y. Feng, L. Li, J. Liu, X. Xu Applied Mathematics Letters 2018. Vol. 83. pdf file
  39. 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
  40. p-Euler equations and p-Navier-Stokes equations
    L. Li, J. Liu J. Differ. Equations 2018. Volume 264, Issue 7 pdf file
  41. 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
  42. Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
    L. Li, J. Liu, J. Lu J. Stat. Phys. 2017. Vol. 169, Issue 2.pdf file
  43. 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
  44. 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
  45. 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
  46. 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
  47. 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
  48. The sedimentation of flexible filaments
    L. Li, H. Manikantan, D. Saintillan, S. E. Spagnolie. Journal of fluid mechanics. 2013. Vol 735. 705-736pdf file

Book chapters, thesis

  1. Random Batch Methods for classical and quantum interacting particle systems and statistical samplings
    S. Jin, L. Li Active particles, Bellomo (ed.), Accepted
  2. Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
    Thesis, UW-Madison, 2015.