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
A class of monotonicity-preserving variable-step discretizations for Volterra integral equations and time fractional ordinary differential equations
Y. Feng, L. Li
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
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
Publications
- On the convergence of continuous and discrete unbalanced optimal transport modelsZ. Xiong, L. Li, Y.-N. Zhu, X. Zhang SIAM J. Numer. Anal. Accepted
- Existence of weak solutions to p-Navier-Stokes equationsY. Feng, L. Li, J. Liu, X. Xu DCDS-B Accepted
- Ergodicity and long-time behavior of the Random Batch Method for interacting particle systemsS. Jin, L. Li, X. Ye and Z. Zhou Mathematical Models and Methods in Applied Sciences 2023, Vol. 33, No. 1 pdf file
- Energy and quadratic invariants preserving methods for Hamiltonian systems with holonomic constraintsL. Li, D. Wang J. Comput. Math. 2023, Vol. 41, No. 1 pdf file
- A splitting Hamiltonian Monte Carlo method for efficient samplingL. 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 ensembleJ. 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 ModelL. 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 equationsL. 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 systemsS. 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 equationsL. 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 systemsS. Jin, L. Li. Science China Mathematics 2022. Vol. 65, Issue 1.pdf file
- Superscalability of the random batch Ewald methodJ. 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 epidemicY. Feng, G. Iyer, L. Li. J. Math. Biology 2021. 82(69), 1-17pdf file
- A random batch Ewald method for particle systems with Coulomb interactionsS. 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 mixtureL. 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 ODEsL. 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 weightsS. 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 problemsJ. 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 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
- Random batch methods (RBM) for interacting particle systemsS. 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 3DL. 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 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
Book chapters, thesis
- Random Batch Methods for classical and quantum interacting particle systems and statistical samplingsS. Jin, L. Li Active particles, Bellomo (ed.), Accepted
- Asymptotic and numerical analysis of fluid-structure interactions at different Reynolds numbers.Thesis, UW-Madison, 2015.