Preprints

A generative sampler for distributions with possible discrete parameter based on reversibility
L. Li, Z. Wang, L. Zhang
Ergodicity and error estimate of laws for a random splitting Langevin Monte Carlo
L. Li, C. Wang, M. Wang
A collision-oriented interacting particle system for Landau-type equations and the molecular chaos
K. Du, L. Li
Propagation of chaos in path spaces via information theory
L. Li, Y. Wang, Y. Wang
Fluctuation suppression and enhancement in interacting particle systems
J. Chen and L. Li

Publications

  1. A generalized discontinuous Hamilton Monte Carlo for transdimensional sampling
    L. Li, X. Luo, Y. Luo Journal of Scientific Computing Accepted
  2. Random ordinate method for mitigating the ray effect in radiative transport equation simulations
    L. Li, M. Tang, Y. Yang SIAM J. Sci. Comput. Accepted
  3. On the discrete Poincare inequality for B-schemes of 1D Fokker-Planck equations in full space
    L. Li, J. Liu, Z. Wang Quarterly Appl. Math. accepted
    A special issue delicated to Prof. Paul Dupuis on occasion of his 65th birthday
  4. Estimates of the numerical density for stochastic differential equations with multiplicative noise
    L. Li, M. Wang, Y. Wang Science China Mathematics Accepted
  5. Solving Schr\"oinger bridge problem via continuous normalizing flow
    Y. Jing, L. Li, J. Zhang East Asian Journal on Applied Mathematics 2026, Vol. 16, No. 4, pp 679--713
  6. Random Source Iteration Method: Mitigating the Ray Effect in the Discrete Ordinates Method
    J. Fu, L. Li, M. Tang SIAM J. Numer. Anal. 2026, Vol. 64, Iss. 1
  7. Convergence of random splitting method for the Allen-Cahn equation in a background flow
    L. Li, C. Wang Numerical Methods for Partial Differential Equations 2025, Vol. 41, Issue 6, e70040
  8. A structure-preserving collisional particle method for the Landau kinetic equation
    K. Du, L. Li, Y. Xie, Y. Yu Journal of Computational Physics 2025, Vol. 543, 114387
  9. A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamics
    L. Li, Y. Wang CSIAM Trans. Appl. Math. 2025, Vol. 6, No. 4, pp. 711-759
  10. A second order Langevin sampler preserving positive volume for isothermal isobaric ensemble
    L. Li， Y. Peng Communications in Computational Physics 2025， Vol. 38, Iss. 3
  11. Convergence analysis of OT-Flow for sample generation
    Y. Jing, L. Li Numer. Math. Theor. Meth. Appl. 2025, Vol. 18, No. 2, pp. 325-352 pdf file
  12. Response to “Comment on ‘A random batch Ewald method for charged particles in the isothermal–isobaric ensemble’” [J. Chem. Phys. 162, 177101 (2025)]
    J. Liang, P. Tan, L. Hong, S. Jin, Z. Xu, L. Li The Journal of Chemical Physics 2025, Vol. 162, 177102
  13. Comment on "Pressure of Coulomb systems with volume-dependent long-range potentials"
    L. Li, J. Liang, Z. Xu. Journal of Physics A: Mathematical and Theoretical 2025, Vol. 58, 088001
    An arxiv version named "A note on accurate pressure calculations of Coulomb systems with periodic boundary conditions" arXiv:2406.05627
  14. Mean field error estimate of the random batch method for large interacting particle system
    Z. Huang, S. Jin, L. Li ESAIM: M2AN 2025, Vol. 59, No. 1, pp. 265–289
  15. Solving stationary nonlinear Fokker-Planck equations via sampling
    L. Li, Y. Tang, J. Zhang SIAM J. Appl. Math. 2025, Vol. 85, No. 1 pdf file
  16. Geometric ergodicity of SGLD via reflection coupling
    L. Li, J.-G. Liu, Y. Wang Stochastics and Dynamics 2024, Vol. 24, No. 5 pdf file
  17. Some Gr\"onwall inequalities for a class of discretizations of time fractional equations on nonuniform meshes
    Y. Feng, L. Li, J. Liu, T. Tang SIAM J. Numer. Anal. 2024, Vol. 62, No. 5, pp. 2196--2221 pdf file
  18. On the completely positive kernels for nonuniform meshes
    Y. Feng, L. Li Quarterly of Applied Mathematics 2024, Vol 82, No. 4, pp. 801--817
  19. A class of monotonicity-preserving variable-step discretizations for Volterra integral equations
    Y. Feng, L. Li BIT Numerical Mathematics 2024， Vol. 64, Iss. 3 pdf file
  20. 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 2024,Vol 58,No. 2, pp. 639--671 pdf file
  21. 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
  22. 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
  23. 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
  24. On uniform-in-time diffusion approximation for stochastic gradient descent
    L. Li, Y. Wang Methods and Applications of Analysis 2023, Vol. 30, No. 3
  25. 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
  26. 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
  27. 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
  28. 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
    An erratum for a sign typo at "J. Chem. Phys. 161 (18), 189901 (2024)"
  29. 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
  30. 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
  31. 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
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. 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
  38. 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
  39. 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
  40. 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
  41. 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. 325, 2283--2320 pdf file
  42. 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
  43. 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
  44. 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
  45. 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
  46. Random batch methods (RBM) for interacting particle systems
    S. Jin, L. Li, J. Liu J. Comput. Phys. 2020. Vol. 400, No. 1 pdf file
  47. 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
  48. 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
  49. 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
  50. 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
  51. 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
  52. 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
  53. 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
  54. 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
  55. 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
  56. A note on one-dimensional time fractional ODEs
    Y. Feng, L. Li, J. Liu, X. Xu Applied Mathematics Letters 2018. Vol. 83. pdf file
  57. 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
  58. p-Euler equations and p-Navier-Stokes equations
    L. Li, J. Liu J. Differ. Equations 2018. Volume 264, Issue 7 pdf file
  59. 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
  60. Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
    L. Li, J. Liu, J. Lu J. Stat. Phys. 2017. Vol. 169, Issue 2.pdf file
  61. 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
  62. 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
  63. 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
  64. 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
  65. 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
  66. 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, reviews and others

  1. Multiscale Physical Problems: asymptotics and asymptotic-preserving schemes
    S. Jin, L. Li. L. Wang, Z. Zhou Kinetic Theory-Analysis, computation and applications (Mario Pulvirenti, Shi Jin (eds)) Numero 65, 2025
  2. 交互作用粒子系统的分析与计算研究进展
    李磊,凌舒扬, 王振富 中国基础科学(China Basic Science) 2023, Iss 4
  3. Random Batch Methods for classical and quantum interacting particle systems and statistical samplings
    S. Jin, L. Li Active particles (Bellomo, Carrillo, Tadmor (ed.))2022, Vol. 3, pp. 153--200
  4. Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
    Thesis, UW-Madison, 2015.