Preprints

Publications

1. A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamics
   L. Li, Y. Wang CSIAM Trans. Appl. Math. Accepted
2. Convergence analysis of OT-Flow for sample generation
   Y. Jing, L. Li Numer. Math. Theor. Meth. Appl. Accepted
3. 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
4. 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
5. 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
6. Solving stationary nonlinear Fokker-Planck equations via sampling
   L. Li, Y. Tang, J. Zhang SIAM J. Appl. Math. 2025, Vol. 85, No. 1
7. Geometric ergodicity of SGLD via reflection coupling
   L. Li, J.-G. Liu, Y. Wang Stochastics and Dynamics 2024, Vol. 24, No. 5
8. 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
9. On the completely positive kernels for nonuniform meshes
   Y. Feng, L. Li Quarterly of Applied Mathematics 2024, Vol 82, No. 4, pp. 801--817
10. 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
11. 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
12. 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
13. 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
14. 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
15. On uniform-in-time diffusion approximation for stochastic gradient descent
    L. Li, Y. Wang Methods and Applications of Analysis 2023, Vol. 30, No. 3
16. 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
17. 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
18. 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
19. 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)"
20. 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
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
32. 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
33. 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
34. 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
35. 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
36. 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
37. Random batch methods (RBM) for interacting particle systems
    S. Jin, L. Li, J. Liu J. Comput. Phys. 2020. Vol. 400, No. 1 pdf file
38. 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
39. 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
40. 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
41. 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
42. 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
43. 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
44. 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
45. 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
46. 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
47. A note on one-dimensional time fractional ODEs
    Y. Feng, L. Li, J. Liu, X. Xu Applied Mathematics Letters 2018. Vol. 83. pdf file
48. 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
49. p-Euler equations and p-Navier-Stokes equations
    L. Li, J. Liu J. Differ. Equations 2018. Volume 264, Issue 7 pdf file
50. 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
51. Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
    L. Li, J. Liu, J. Lu J. Stat. Phys. 2017. Vol. 169, Issue 2.pdf file
52. 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
53. 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
54. 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
55. 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
56. 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
57. 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. 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
2. 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
3. Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
   Thesis, UW-Madison, 2015.