Batch Size Matters: A Diffusion Approximation Framework on Nonconvex Stochastic Gradient Descent. - Chris Junchi Li; Lei Li 006; Junyang Qian; Jian-Guo Liu 006 (CoRR, 2017)

A Modified Levy Jump-Diffusion Model Based on Market Sentiment Memory for Online Jump Prediction. - Zheqing Zhu; Jian-Guo Liu 006; Lei Li 006 (CoRR, 2017)

A Locally Gradient-Preserving Reinitialization for Level Set Functions. - Lei Li 006; Xiaoqian Xu; Saverio E. Spagnolie (J. Sci. Comput., 2017)

A note on one-dimensional time fractional ODEs. - Yuanyuan Feng; Lei Li 006; Jian-Guo Liu 006; Xiaoqian Xu (Appl. Math. Lett., 2018)

A Dispersive Regularization for the Modified Camassa-Holm Equation. - Yu Gao; Lei Li 006; Jian-Guo Liu 006 (SIAM J. Math. Anal., 2018)

A Generalized Definition of Caputo Derivatives and Its Application to Fractional ODEs. - Lei Li 006; Jian-Guo Liu 006 (SIAM J. Math. Anal., 2018)

Some Compactness Criteria for Weak Solutions of Time Fractional PDEs. - Lei Li 006; Jian-Guo Liu 006 (SIAM J. Math. Anal., 2018)

Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation. - Yuanyuan Feng; Tingran Gao; Lei Li 006; Jian-Guo Liu 006; Yulong Lu (CoRR, 2019)

A stochastic version of Stein Variational Gradient Descent for efficient sampling. - Lei Li 006; Jian-Guo Liu 006; Zibu Liu; Jianfeng Lu 001 (CoRR, 2019)

A Discretization of Caputo Derivatives with Application to Time Fractional SDEs and Gradient Flows. - Lei Li 006; Jian-Guo Liu 006 (SIAM J. Numer. Anal., 2019)

A direct simulation approach for the Poisson-Boltzmann equation using the Random Batch Method. - Lei Li 006; Jian-Guo Liu 006; Yijia Tang (CoRR, 2020)

On the mean field limit of Random Batch Method for interacting particle systems. - Shi Jin 003; Lei Li 006 (CoRR, 2020)

Random Batch Methods (RBM) for interacting particle systems. - Shi Jin 003; Lei Li 006; Jian-Guo Liu 006 (J. Comput. Phys., 2020)

Large time behaviors of upwind schemes and B-schemes for Fokker-Planck equations on ℝ by jump processes. - Lei Li 006; Jian-Guo Liu 006 (Math. Comput., 2020)

A Random-Batch Monte Carlo Method for Many-Body Systems with Singular Kernels. - Lei Li 006; Zhenli Xu; Yue Zhao (SIAM J. Sci. Comput., 2020)

Random Batch Methods for classical and quantum interacting particle systems and statistical samplings. - Shi Jin 003; Lei Li 006 (CoRR, 2021)

Super-Scalable Molecular Dynamics Algorithm. - Jiuyang Liang; Pan Tan; Yue Zhao; Lei Li 006; Shi Jin 003; Liang Hong; Zhenli Xu (CoRR, 2021)

Convergence of the Random Batch Method for Interacting Particles with Disparate Species and Weights. - Shi Jin 003; Lei Li 006; Jian-Guo Liu 006 (SIAM J. Numer. Anal., 2021)

A Random Batch Ewald Method for Particle Systems with Coulomb Interactions. - Shi Jin 003; Lei Li 006; Zhenli Xu; Yue Zhao (SIAM J. Sci. Comput., 2021)

A deep learning framework for geodesics under spherical Wasserstein-Fisher-Rao metric and its application for weighted sample generation. - Yang Jing; Jiaheng Chen; Lei Li 006; Jianfeng Lu 001 (CoRR, 2022)

On the Random Batch Method for Second Order Interacting Particle Systems. - Shi Jin 003; Lei Li 006; Yiqun Sun (Multiscale Model. Simul., 2022)

A class of monotonicity-preserving variable-step discretizations for Volterra integral equations and time fractional ordinary differential equations. - Yuanyuan Feng; Lei Li 006 (CoRR, 2023)

On the completely positive kernels for nonuniform meshes. - Yuanyuan Feng; Lei Li 006 (CoRR, 2023)

Convergence analysis of OT-Flow for sample generation. - Yang Jing; Lei Li 006 (CoRR, 2024)

Some Grönwall Inequalities for a Class of Discretizations of Time Fractional Equations on Nonuniform Meshes. - Yuanyuan Feng; Lei Li 006; Jian-Guo Liu 006; Tao Tang (SIAM J. Numer. Anal., 2024)

On the Convergence of Continuous and Discrete Unbalanced Optimal Transport Models for 1-Wasserstein Distance. - Zhe Xiong; Lei Li 006; Ya-Nan Zhu; Xiaoqun Zhang (SIAM J. Numer. Anal., 2024)

A Machine Learning Framework for Geodesics Under Spherical Wasserstein-Fisher-Rao Metric and Its Application for Weighted Sample Generation. - Yang Jing; Jiaheng Chen; Lei Li 006; Jianfeng Lu 001 (J. Sci. Comput., 2024)

Solving Stationary Nonlinear Fokker-Planck Equations via Sampling. - Lei Li 006; Yijia Tang; Jingtong Zhang (SIAM J. Appl. Math., 2025)