About
I'm a tenure track Associate Professor at Shanghai Jiao Tong University. My interest lies in applied math, including
- Computational Math (random algorithms, numerical SDEs and PDEs)
- Analysis of differential equations (PDE models, optimal transport etc, time fractional differential equations)
- Fluid-Structure interaction
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.
Preprints
On the Random Batch Method for second order interacting particle systems
S. Jin, L. Li, Y. Sun
A random batch Ewald method for particle systems with Coulomb interactions
S. Jin, L. Li, Z. Xu, Y. Zhao
Scheduling fixed length quarantines to minimize the total number of fatalities during an epidemic
Y. Feng, G. Iyer, L. Li
Energy and quadratic invariants preserving methods for Hamiltonian systems with holonomic constraints
L. Li, D. Wang
A direct simulation approach for the Poisson-Boltzmann equation using the Random Batch Method
L. Li, J. Liu, Y. Tang
Numerical methods for stochastic differential equations based on Gaussian mixture
L. Li, J. Lu, J. Mattingly, L. Wang
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
Publications
- Complete Monotonicity-preserving numerical methods for time fractional ODEsL. Li, D. Wang Comm. Math. Sci. Accepted
- Convergence of Random Batch Method for interacting particles with disparate species and weightsS. Jin, L. Li, J. Liu SIAM J. Numer. Anal. Accepted
- On the mean field limit of Random Batch Method for interacting particle systemsS. Jin, L. Li Science China Mathematics Accepted
- A consensus-based global optimization method for high dimensional machine learning problemsJ. A. Carrillo, S. Jin, L. Li, Y. Zhu ESAIM: Control, Optimisation and Calculus of Variations Accepted
- Large time behaviors of upwind schemes and B-schemes for Fokker-Planck equations on R by jump processesL. Li, J. Liu Math. Comp. 2020. Vol. 89, No. 235, 2283--2320 pdf file
- A stochastic version of Stein Variational Gradient Descent for efficient samplingL. 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 kernelsL. 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 ApproximationY. 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 noiseD. Fang, L. Li ESAIM: Math. Model. Numer. Anal. 2020. Vol. 54, No. 2, 431-463 pdf file
- On the mean field limit for Brownian particles with Coulomb interaction in 3DL. Li, J. Liu, P. Yu J. Math. Phys. 2019. Vol. 60. 111501 pdf file
- Random batch methods (RBM) for interacting particle systemsS. Jin, L. Li, J. Liu J. Comput. Phys. 2020. Vol. 400, No. 1 pdf file
- A discretization of Caputo derivatives with application to time fractional SDEs and gradient flowsL. 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 equationY. Gao, L. Li, J. Liu Physica D: Nonlinear Phenomena 2019. Vol. 390. 15-35 pdf file
- On the diffusion approximation of nonconvex stochastic gradient descentW. 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 approximationsY. Feng, L. Li, J. Liu Comm. Math. Sci. 2018. Vol. 16, No. 3 pdf file
- Some compactness criteria for weak solutions of time fractional PDEsL. 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 ODEsL. Li, J. Liu SIAM: J. Math. Anal. 2018. Vol. 50, Issue 3. 2867-2900pdf file
- A dispersive regularization for the modified Camassa-Holm equationY. 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 equationL. Li, J. Liu, L. Wang J. Differ. Equations 2018. Vol. 265, Issue 3 pdf file
- A note on one-dimensional time fractional ODEsY. Feng, L. Li, J. Liu, X. Xu Applied Mathematics Letters 2018. Vol. 83. pdf file
- Continuous and discrete one dimensional autonomous fractional ODEsY. 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 equationsL. Li, J. Liu J. Differ. Equations 2018. Volume 264, Issue 7 pdf file
- A note on deconvolution with completely monotone sequences and discrete fractional calculusL. Li, J. Liu Quart. Appl. Math. 2018. Vol. 76, Issue 1 pdf file
- Fractional stochastic differential equations satisfying fluctuation-dissipation theoremL. Li, J. Liu, J. Lu J. Stat. Phys. 2017. Vol. 169, Issue 2.pdf file
- A locally gradient preserving reinitialization for level set functionsL. 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 fluidsL. Li, S. E. Spagnolie Physics of fluids. 2015. Vol. 27, Issue 2.pdf file
- Analytical solution for laterally loaded long piles basedon Fourier-Laplace integralF. 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 fibresH. Manikantan, L. Li, S. E. Spagnolie, D. Saintillan. Journal of fluid mechanics. 2014. Vol 756. 935-964pdf file
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Swimming and pumping of rigid helical bodies in viscous fluidsL. Li, S. E. Spagnolie, Physics of fluids. 2014. Vol. 26, Issue 4.pdf file
- The sedimentation of flexible filamentsL. Li, H. Manikantan, D. Saintillan, S. E. Spagnolie. Journal of fluid mechanics. 2013. Vol 735. 705-736pdf file
Thesis
Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.
2015. UW-Madison.