### Preprints

- with Lei Li, Jonathan Mattingly, and Lihan Wang,
*Numerical methods for stochastic differential equations based on Gaussian mixture*(2018) [arXiv:1812.11932] - with Christopher D. Sogge and Stefan
Steinerberger,
*Approximating pointwise products of Laplacian eigenfunctions*(2018) [arXiv:1811.10447] - with Zhennan Zhou,
*Continuum limit and preconditioned Langevin sampling for the path integral molecular dynamics*(2018) [arXiv:1811.10995] - with Zhenning Cai and Siyao Yang,
*Inchworm Monte Carlo method for open quantum systems*(2018) [arXiv:1811.08044] - with Hongxu Chen and Qin Li,
*Numerical coupling methods of BGK model and Euler equation through linerized Knudsen layer*(2018) [arXiv:1811.03041] - with Kyle Thicke and Alex Watson,
*Computation of bound states of semi-infinite matrix Hamiltonians with applications to edge states of two-dimensional materials*(2018) [arXiv:1810.07082] - with Yu Cao and Yulong Lu,
*Gradient flow structure and exponential decay of the sandwiched Rényi divergence for primitive Lindblad equations with GNS-detailed balance*(2018) [arXiv:1810.00906] - with Alex Watson and Michael I. Weinstein,
*Dirac operators and domain walls*(2018) [arXiv:1808.01378] - with Ke Chen, Qin Li, and Stephen J. Wright,
*Random sampling and efficient algorithms for multiscale PDEs*(2018) [arXiv:1807.08848] - with Yingzhou Li and Zhe Wang,
*Cooridnate-wise descent methods for leading eigenvalue problem*(2018) [arXiv:1806.05647] - Yingzhou Li, Xiuyuan Cheng, and Jianfeng
Lu,
*Butterfly-Net: Optimal function representation based on convolutional neural networks*(2018) [arXiv:1805.07451] - with Jing An and Lexing Ying,
*Stochastic modified equations for the asynchronous stochastic gradient descent*(2018) [arXiv:1805.08244] - Wei Zhu, Qiang Qiu, Bao Wang, Jianfeng Lu, Guillermo
Sapiro, and Ingrid Daubechies,
*Stop memorizing: A data-dependent regularization framework for intrinsic pattern learning*(2018) [arXiv:1805.07291] - with Yu Cao and Yulong Lu,
*Exponential decay of Rényi divergence under Fokker-Planck equations*(2018) [arXiv:1805.06544] - with Matthias Sachs and Stefan
Steinerberger,
*Quadrature Points via Heat Kernel Repulsion*(2018) [arXiv:1804.02327] - with Felix Otto,
*Optimal artificial boundary condition for elliptic random media*(2018) [arXiv:1803.09593] - with Zhenning Cai and Kevin Stubbs,
*On discrete Wigner transforms*(2018) [arXiv:1802.05834] - with Ke Chen, Qin Li, and Stephen
J. Wright,
*Randomized sampling for basis functions construction in generalized finite element methods*(2018) [arXiv:1801.06938] - with Yuehaw Khoo and Lexing Ying,
*Efficient construction of tensor ring representations from sampling*(2017) [arXiv:1711.00954] - with Stefan Steinerberger,
*Riesz energy on the torus: Regularity of minimizers*(2017) [arXiv:1710.08010] - Ling Li, Haizhao Yang, Katherine R. Phillips, Jinjin
Zhong, Jianfeng Lu, and Joanna Aizenberg,
*Microscopic origins of the crystallographically preferred growth in evaporation-induced colloidal crystals*(2017), submitted - with Yuehaw Khoo and Lexing Ying,
*Solving parametric PDE problems with artificial neural networks*(2017) [arXiv:1707.03351] - with David Dunson and Akihiko
Nishimura,
*Discontinuous Hamiltonian Monte Carlo for sampling discrete parameters*(2017) [arXiv:1705.08510] - with Jian-Guo Liu, Dio Margetis, and Jeremy
Marzuola,
*Asymmetry in crystal facet dynamics of homoepitaxy in a continuum model*(2017) [arXiv:1704.01554] - with Zhennan Zhou,
*Bloch dynamics with second order Berry phase correction*(2015) [arXiv:1512.07357] - with Felix Otto,
*An isoperimetric problem with Coulomb repulsion and attraction to a background nucleus*(2015) [arXiv:1508.07172]