### Preprints

- Yingzhou Li, Xiuyuan Cheng, and Jianfeng
Lu,
*Butterfly-Net: Optimal function represention based on convolutional neural networks*[arXiv:1805.07451] (2018) - with Jing An and Lexing Ying,
*Stochastic modified equations for the asynchronous stochastic gradient descent*[arXiv:1805.08244] (2018) - Wei Zhu, Qiang Qiu, Bao Wang, Jianfeng Lu, Guillermo
Sapiro, and Ingrid Daubechies,
*Stop memorizing: A data-dependent regularization framework for intrinsic pattern learning*[arXiv:1805.07291] (2018) - with Yu Cao and Yulong Lu,
*Exponential decay of Rényi divergence under Fokker-Planck equations*(2018) [arXiv:1805.06544] - with Yulong Lu and Jim Nolen,
*Scaling limit of the Stein variational gradient descent part I: the mean field regime*(2018) [arXiv:1805.04035] - with Felix Otto,
*Optimal artificial boundary condition for elliptic random media*(2018) [arXiv:1803.09593] - with Yuehaw Khoo and Lexing Ying,
*Solving for high dimensional committor functions using artificial neural networks*(2018) [arXiv:1802.10275] - with Yu Cao,
*Stochastic dynamical low-rank approximation method*(2018) [arXiv:1803.00499] - with Zhenning Cai and Kevin Stubbs,
*On discrete Wigner transforms*(2018) [arXiv:1802.05834] - with Thomas Barthel,
*Fundamental limitations for measurements in quantum many-body systems*(2018) [arXiv:1802.04378] - with Hui Huang and Jian-Guo Liu,
*Learning interacting particle system: diffusion parameter estimation for aggregation equations*(2018) [arXiv:1802.02267] - 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 Eric Vanden-Eijnden,
*Methodological and computational aspects of parallel tempering methods in the infinite swapping limit*(2017) [arXiv:1712.06947] - with Zhe Wang,
*The full configuration interaction quantum Monte Carlo method in the lens of inexact power iteration*(2017) [arXiv:1711.09153] - 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 Yingzhou Li,
*Bold diagrammatic Monte Carlo in the lens of stochastic iterative methods*(2017) [arXiv:1710.00966] - with Stefan Steinerberger,
*Detecting localized eigenstates of linear operators*(2017) [arXiv:1709.03364] - with Yuehaw Khoo and Lexing Ying,
*Solving parametric PDE problems with artificial neural networks*(2017) [arXiv:1707.03351] - with Di Fang,
*A diabatic surface hopping algorithm based on time dependent perturbation theory and semiclassical analysis*(2017) [arXiv:1707.00765] - with David Dunson and Akihiko Nishimura,
*Discontinuous Hamiltonian Monte Carlo for sampling discrete parameters*(2017) [arXiv:1705.08510] - with Zhenning Cai,
*A surface hopping Gaussian beam method for high-dimensional transport systems*(2017) [arXiv:1703.06116] - 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 Konstantinos Spiliopoulos,
*Analysis of multiscale integrators for multiple attractors and irreversible Langevin samplers*(2016) [arXiv:1606.09539] - 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]