个人简介
Institute of Natural Sciences; School of mathematical sciences.
Shanghai Jiao Tong University
Office: 323 Science Building No. 5
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.
About
I'm a tenure track Associate Professor at Shanghai Jiao Tong University. My interest lies in applied math, including
Scientific Computing (random algorithms for particle systems and machine learning etc, numerical SDEs and PDEs)
Applied Analysis (time fractional differential equations, PDE models, optimal transport etc)
Fluid-Structure interaction
Here is my CV.
Positions
Tenure track Associate Professor, SJTU; 2018-present
Assistant Research Professor, Duke University, 2015-2018
Education
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.
Links
Study seminar on many-body systems
Preprints
Geometric ergodicity of SGLD via reflection coupling
L. Li, J.-G. Liu, Y. Wang
A deep 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
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
On uniform-in-time diffusion approximation for stochastic gradient descent
L. Li, Y. Wang
Book chapters, thesis
Random Batch Methods for classical and quantum interacting particle systems and statistical samplings
S. Jin, L. Li Active particles, Bellomo (ed.), Accepted
Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
Thesis, UW-Madison, 2015.
近期论文
查看导师新发文章
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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 Accepted
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Random batch methods (RBM) for interacting particle systems
S. Jin, L. Li, J. Liu J. Comput. Phys. 2020. Vol. 400, No. 1 pdf file
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
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
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
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
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
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
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
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
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
A note on one-dimensional time fractional ODEs
Y. Feng, L. Li, J. Liu, X. Xu Applied Mathematics Letters 2018. Vol. 83. pdf file
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
p-Euler equations and p-Navier-Stokes equations
L. Li, J. Liu J. Differ. Equations 2018. Volume 264, Issue 7 pdf file
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
Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
L. Li, J. Liu, J. Lu J. Stat. Phys. 2017. Vol. 169, Issue 2.pdf file
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
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
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
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
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
The sedimentation of flexible filaments
L. Li, H. Manikantan, D. Saintillan, S. E. Spagnolie. Journal of fluid mechanics. 2013. Vol 735. 705-736pdf file
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