I'm a tenure track Associate Professor at Shanghai Jiao Tong University. My interest lies in applied math, including
- Analysis of differential equations (PDE models, optimal transport etc, time fractional differential equations)
- Numerical SDEs and PDEs
- Fluid-Structure interaction
Tenure track Associate Professor, SJTU; 2018-present
Assistant Research Professor, Duke University, 2015-2018
2010-2015. Mathematics. Phd. UW-Madison.
Major: Applied math; Minor: Probability and analysis; Advisor: Saverio Spagnolie
2013. Mathematics. MA. UW-Madison
2012. Computer Science. MS. UW-Madison.
2006-2010. Mathematics and Physics(基科) (applied). BS. Tsinghua University, Beijing.
A stochastic version of Stein Variational Gradient Descent for efficient sampling
L. Li, J. Liu, Z. Liu, J. Lu
Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation
Y. Feng, T. Gao, L. Li, J. Liu, Y. Lu
A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows
L. Li, J. Liu
Numerical methods for stochastic differential equations based on Gaussian mixture
L. Li, J. Lu, J. Mattingly, L. Wang
Random batch methods (RBM) for interacting particle systems
S. Jin, L. Li, J. Liu
On mean field limit for Brownian particles with Coulomb interaction in 3D
L. Li, J. Liu, P. Yu
Numerical study of ergodicity for the overdamped generalized Langevin equation with fractional noise
D. Fang, L. Li
Large time behaviors of upwind schemes by jump processes
L. Li, J. Liu
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
Patched peakon weak solutions of the modified Camassa-Holm equation
Y. Gao, L. Li, J. Liu Physica D To appear
On the diffusion approximation of nonconvex stochastic gradient descent
W. Hu, C. J. Li, L. Li, J. Liu Annals of Mathematical Sciences and Applications To appear
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
Some compactness criteria for weak solutions of time fractional PDEs
L. Li, J. Liu SIAM: Math. Anal. 2018. Vol. 50, Issue 4. 3963-3995
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. 2867-2900
A dispersive regularization for the modified Camassa-Holm equation
Y. Gao, L. Li, J. Liu SIAM J. Math. Anal.
2018. Vol. 50, Issue 3. 2807-2838
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
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
p-Euler equations and p-Navier-Stokes equations
L. Li, J. Liu J. Differ. Equations
2018. Volume 264, Issue 7
A note on deconvolution with completely monotone sequences and discrete fractional calculus
L. Li, J. Liu Quart. Appl. Math.
2018. Vol. 76, Issue 1
Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
L. Li, J. Liu, J. Lu J. Stat. Phys.
2017. Vol. 169, Issue 2.
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.
Analytical solution for laterally loaded long piles based
on 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. 935-964
Swimming and pumping of rigid helical bodies in viscous fluids
L. Li, S. E. Spagnolie, Physics of fluids.
2014. Vol. 26, Issue 4.
The sedimentation of flexible filaments
L. Li, H. Manikantan, D. Saintillan, S. E. Spagnolie.
Journal of fluid mechanics.
2013. Vol 735. 705-736
Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
Shanghai Jiao Tong U.
Advanced Computational Methods, Fall, 2018
- MATH 660 -Intro. Numer. PDEs, Spring, 2018
- MATH 212 -Multivariable Calculus, Fall, 2017
- MATH 575 -Mathematical Fluid dynamics, Spring, 2017
- MATH 212 -Multivariable Calculus, Fall, 2016
- MATH 660 -Intro. Numer. PDEs, Spring, 2016
- MATH 212 -Multivariable Calculus, Spring, 2016
- MATH 212 -Multivariable Calculus, Fall, 2015
- MATH 319 -Differential Equations, Spring, 2015
- MATH 234 -Calculus, Fall, 2014
- MATH 320 -Linear algebra and differential equations
- MATH 234 -Calculus, Fall, 2013
- MATH 340 -Elem Matrix&Linear Algebra, Spring, 2013
- MATH 321 - Applied Mathematical Analysis, Fall, 2012
- MATH 321 - Applied Mathematical Analysis, Spring, 2012
- MATH 222 - Calculus and Analytic Geometry, Fall, 2011
- MATH 222 - Calculus and Analytic Geometry, Spring, 2011
- MATH 222 - Calculus and Analytic Geometry, Fall, 2010