Chenyu Wang, Yangshuai Wang, Lei Zhang,
From energy-force weighting to primal-dual optimization of machine-learned interatomic potentials.
arXiv:2610.00876
Wei Zhao, Yangshuo Zou, Chengxiang Ding, Yifan Wu, Xuchuan Wang, Zimu Mao, Lei Zhang, Tao Luo,
Fyan: A human–AI harness with semantic auditing for document-level formalization.
arXiv:2609.39228
Kai Jiang, Meng Li, Juan Zhang, Lei Zhang,
A high-accuracy numerical homogenization method for quasiperiodic Hamilton–Jacobi equations.
arXiv:2608.24313
Siqi Chen, Shi Jin, Lei Zhang,
Young measure based quantum linear programming algorithms for nonlinear/stochastic multiscale partial differential equations and homogenization.
arXiv:2606.06165
Xiang Cao, Qiaoqiao Ding, Xinliang Liu, Xiaoqun Zhang,
Diff-ANO: Towards fast high-resolution ultrasound computed tomography via conditional consistency models and adjoint neural operators.
arXiv:2507.16344
Publications
[64]Zetao Ma, Jingrun Chen, Rui Du, Lei Zhang,
Numerical homogenization of Landau-Lifshitz equation with rough coefficients,
J. Comput. Phys., accepted, 2026.
arXiv:2508.02434
[63]Xinyi Wei, Julian Braun, Yangshuai Wang, Lei Zhang,
Higher-order boundary conditions for atomistic dislocation simulations,
SIAM J. Sci. Comput., accepted, 2026.
arXiv:2510.04751
[62]Shi Jin, Zihao Tang, Xu Yin, Lei Zhang,
Quantum circuits for Black-Scholes equations via Schrödingerisation,
Commun. Comput. Phys., 39(6), 1, 2026.
arXiv:2505.04304
[61]Junpeng Hu, Jianglai Li, Lei Zhang, Shi Jin,
A quantum gradient descent algorithm for optimizing Gaussian process models,
Math. Models Methods Appl. Sci., 36(8), 1715–1737, 2026.
arXiv:2503.17780
[60]Junpeng Hu, Shi Jin, Nana Liu, Lei Zhang,
Quantum random feature method for solving partial differential equations,
Discrete Contin. Dyn. Syst., 55, 497–519, 2026.
arXiv:2510.07945
[59]Chuwen Ma, Shi Jin, Nana Liu, Kezhen Wang, Lei Zhang,
Schrödingerization-based quantum circuits for Maxwell's equations with time-dependent source terms,
J. Sci. Comput., 108, Article 43, 2026.
arXiv:2411.10999
[58]Xinyi Wei, Yangshuai Wang, Kai Jiang, Lei Zhang,
Amplitude expansion phase field crystal (APFC) modeling based efficient dislocation simulations using Fourier pseudospectral method,
J. Sci. Comput., 108, Article 57, 2026.
arXiv:2410.22720
[57]Peng Liu, Lidong Fang, Yangshuai Wang, Lei Zhang, Qingcheng Yang,
Concurrent atomistic-continuum coupling via physics-informed neural networks (PINNs-CAC) with adaptive energy weighting and direct boundary encoding,
Appl. Math. Model., 158, Article 116931, 2026.
[56]Tao Yu, Tailong Jin, Yanfeng Shen, Lei Zhang,
Local interaction simulation approach for the acoustic wave equation with perfectly matched layer,
Adv. Appl. Math. Mech., 18(3), 833–855, 2026.
arXiv:2411.12443
[55]Qinchen Song, Jingyi Fu, Min Tang, Lei Zhang,
An adaptive angular domain compression scheme for solving multiscale radiative transfer equation,
J. Sci. Comput., 104, Article 49, 2025.
DOI ·
arXiv:2408.08783
[54]Kai Jiang, Meng Li, Juan Zhang, Lei Zhang,
Convergence analysis of PM-BDF2 method for quasiperiodic parabolic equations,
J. Sci. Comput., 104, Article 24, 2025.
DOI ·
arXiv:2412.19175
[53]Kai Jiang, Meng Li, Juan Zhang, Lei Zhang,
Projection method for quasiperiodic elliptic equations and application to quasiperiodic homogenization,
SIAM J. Numer. Anal., 63(5), 1962–1985, 2025.
DOI ·
arXiv:2404.06841
[52]Junpeng Hu, Shi Jin, Nana Liu, Lei Zhang,
Dilation theorem via Schrödingerisation, with applications to the quantum simulation of differential equations,
Stud. Appl. Math., 154(4), e70047, 2025.
DOI ·
arXiv:2309.16262
[51]Kejie Fu, Mingjie Liao, Yangshuai Wang, Jianjun Chen, Lei Zhang,
MeshAC: A 3D mesh generation and adaptation package for multiscale coupling methods,
Comput. Phys. Commun., 310, 109523, 2025.
DOI ·
arXiv:2402.09446 ·
Code
[50]Julian Braun, Christoph Ortner, Yangshuai Wang, Lei Zhang,
Higher order far-field boundary conditions for crystalline defects,
SIAM J. Numer. Anal., 63(2), 520–541, 2025.
DOI ·
arXiv:2210.05573
[49]Bo Xu, Xinliang Liu, Lei Zhang,
Dilated convolution neural operator for multiscale partial differential equations,
J. Comput. Appl. Math., 461, 116408, 2025.
DOI ·
arXiv:2408.00775
[48]Junpeng Hu, Shi Jin, Nana Liu, Lei Zhang,
Quantum circuits for partial differential equations via Schrödingerisation,
Quantum, 8, 1563, 2024.
DOI ·
arXiv:2403.10032 ·
Code
[47]Bo Xu, Han Li, Lei Zhang, Helin Gong,
A comprehensive deep learning–based approach to field reconstruction in reactor cores,
Nucl. Sci. Eng., 199, 873–887, 2024.
DOI
[46]Leonid Berlyand, Etienne Sandier, Yitzchak Shmalo, Lei Zhang,
Enhancing accuracy in deep learning using random matrix theory,
J. Mach. Learn., 3(4), 347–412, 2024.
DOI ·
arXiv:2310.03165 ·
Code
[45]Qinshuo Liu, Zixin Wang, Xi'An Li, Xinyao Ji, Lei Zhang, Lin Liu, Zhonghua Liu,
DNA-SE: Towards deep neural-nets assisted semiparametric estimation,
International Conference on Machine Learning (ICML), 2024.
OpenReview ·
arXiv:2408.02045
[44]Ran Chen, Guisen Liu, Peidong Wu, Jian Wang, Lei Zhang, Yao Shen,
Slip-discreteness-corrected strain gradient crystal plasticity (SDC-SGCP) theory,
Int. J. Plast., 180, 104054, 2024.
DOI
[43]Junpeng Hu, Shi Jin, Lei Zhang,
Quantum algorithms for multiscale partial differential equations,
Multiscale Model. Simul., 22(3), 1030–1067, 2024.
DOI ·
arXiv:2304.06902
[42]Yangshuai Wang, James R. Kermode, Christoph Ortner, Lei Zhang,
A posteriori error estimate and adaptivity for QM/MM models of crystalline defects,
Comput. Methods Appl. Mech. Engrg., 428, 117097, 2024.
DOI ·
arXiv:2210.04856
[41]Xinliang Liu, Bo Xu, Lei Zhang,
Mitigating spectral bias for the multiscale operator learning with hierarchical attention,
J. Comput. Phys., 506, 112944, 2024.
DOI ·
arXiv:2210.10890
[40]Zhaoyang Wang, Ping Lin, Lei Zhang,
A fast front-tracking approach and its analysis for a temporal multiscale flow problem with a fractional-order boundary growth,
SIAM J. Sci. Comput., 45(5), B646–B672, 2023.
DOI ·
arXiv:2209.09038
[39]Dereck Olson, Christoph Ortner, Yangshuai Wang, Lei Zhang,
Elastic far-field decay from dislocations in multilattices,
Multiscale Model. Simul., 21(4), 1379–1409, 2023.
DOI ·
arXiv:1910.12269
[38]Xi-An Li, Zhi-Qin John Xu, Lei Zhang,
Subspace decomposition based DNN algorithm for elliptic-type multi-scale PDEs,
J. Comput. Phys., 488, 112242, 2023.
DOI ·
arXiv:2112.06660
[37]Kejie Fu, Mingjie Liao, Yangshuai Wang, Jianjun Chen, Lei Zhang,
Adaptive multigrid strategy for large-scale molecular mechanics optimization,
J. Comput. Phys., 485, 112113, 2023.
DOI ·
arXiv:2105.02672
[36]Junpeng Hu, Shi Jin, Jinglai Li, Lei Zhang,
On multilevel Monte Carlo methods for deterministic and uncertain hyperbolic systems,
J. Comput. Phys., 475, 111847, 2023.
DOI ·
arXiv:2205.06424
[35]Yanping Chen, Xinliang Liu, Lei Zhang, Jiaoyan Zeng,
Optimal control for multiscale PDEs with rough coefficients,
J. Comput. Math., 41, 842–866, 2023.
DOI ·
arXiv:1901.10624
[34]Jingrun Chen, Rui Du, Zetao Ma, Zhiwei Sun, Lei Zhang,
On the multiscale Landau-Lifshitz-Gilbert equation: Two-scale convergence and stability analysis,
Multiscale Model. Simul., 20(2), 835–856, 2022.
DOI
[33]Lidong Fang, Pei Ge, Lei Zhang, Huan Lei, Weinan E,
DeePN2: A deep learning-based non-Newtonian hydrodynamic model,
J. Mach. Learn., 1, 114–140, 2022.
DOI ·
arXiv:2112.14798
[32]Xinliang Liu, Lei Zhang, Shengxin Zhu,
Generalized rough polyharmonic splines for multiscale PDEs with rough coefficients,
Numer. Math. Theory Methods Appl., 14, 862–892, 2021.
DOI ·
arXiv:2103.01788
[31]Xinliang Liu, Eric Chung, Lei Zhang,
Iterated numerical homogenization for multi-scale elliptic equations with monotone nonlinearity,
Multiscale Model. Simul., 19(4), 1601–1632, 2021.
DOI ·
arXiv:2101.00818
[30]Yangshuai Wang, Huajie Chen, Mingjie Liao, Christoph Ortner, Hao Wang, Lei Zhang,
A posteriori error estimates for adaptive QM/MM coupling methods,
SIAM J. Sci. Comput., 43(4), A2785–A2808, 2021.
DOI ·
arXiv:2007.05260
[29]Lidong Fang, Lei Zhang,
Blended ghost force correction method for 3d crystalline defects,
Commun. Comput. Phys., 29, 1246–1272, 2021.
DOI ·
arXiv:2006.06501
[28]Yangshuai Wang, Hao Wang, Lei Zhang,
A priori analysis of a higher order nonlinear elasticity model for an atomistic chain with periodic boundary condition,
IMA J. Numer. Anal., 41(2), 1465–1495, 2021.
DOI ·
arXiv:1905.07110
[27]Xi'an Li, Zhiqin John Xu, Lei Zhang,
A DNN-based algorithm for multi-scale elliptic problems,
Commun. Comput. Phys., 28, 1886–1906, special issue on “Machine Learning for Scientific Computing”, 2020.
DOI ·
arXiv:2009.14597
[26]Hai Chi, Mikhailo Potomkin, Lei Zhang, Igor Aronson, Leonid Berlyand,
Surface anchoring controls orientation of a microswimmer in nematic liquid crystal,
Commun. Phys., 3, Article 162, 2020.
DOI
[25]Lidong Fang, Apala Majumdar, Lei Zhang,
Surface, size and topological effects for some nematic equilibria on rectangular domains,
Math. Mech. Solids, 25(5), 1101–1123, 2020.
DOI ·
arXiv:1907.04195
[24]Haolei Wang, Lei Zhang,
Energy minimization and preconditioning in the simulation of athermal granular materials in two dimensions,
Electron. Res. Arch., 28(1), 405–421, 2020.
DOI ·
arXiv:1911.08305
[23]Mingjie Liao, Ping Lin, Lei Zhang,
A posteriori error estimate and adaptive mesh refinement algorithm for atomistic/continuum coupling with finite range interactions in two dimensions,
Commun. Comput. Phys., 27, 198–226, 2020.
DOI ·
arXiv:1806.11106
[22]Hehu Xie, Lei Zhang, Houman Owhadi,
Fast eigenpairs computation with operator adapted wavelets and hierarchical subspace correction,
SIAM J. Numer. Anal., 57(6), 2519–2550, 2019.
DOI ·
arXiv:1806.00565
[21]Huajie Chen, Mingjie Liao, Hao Wang, Yangshuai Wang, Lei Zhang,
Adaptive QM/MM coupling for crystalline defects,
Comput. Methods Appl. Mech. Engrg., 354, 351–368, 2019.
DOI ·
arXiv:1812.00145
[20]Haiting Liu, Ran Chen, Mao Wen, Lei Zhang, Yao Shen,
Optimizing parallel section length for small tensile specimen with fabrication non-uniformity in thickness,
Fusion Eng. Des., 147, 111244, 2019.
DOI
[19]Hao Wang, Mingjie Liao, Ping Lin, Lei Zhang,
A posteriori error estimation and adaptive algorithm for the atomistic/continuum coupling in 2D,
SIAM J. Sci. Comput., 40(4), A2087–A2119, 2018.
DOI ·
arXiv:1702.02701
[18]Ling Zhang, Jie Zheng, Yinqiao Wang, Lei Zhang, Zhaohui Jin, Liang Hong, Yujie Wang, Jie Zhang,
Experimental studies of vibrational modes in a two-dimensional amorphous solid,
Nature Commun., 8, Article 67, 2017.
DOI
[17]Houman Owhadi, Lei Zhang,
Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients,
J. Comput. Phys., 347, 99–128, 2017.
DOI ·
arXiv:1606.07686
[16]Haiting Liu, Yao Sheng, Shuang Yang, Pengfei Zheng, Lei Zhang,
A comprehensive solution to miniaturized tensile testing: Specimen geometry optimization and extraction of constitutive behaviors using inverse FEM procedure,
Fusion Eng. Des., 121, 188–197, 2017.
[15]Matthew S. Mizuhara, Leonid Berlyand, Volodymyr Rybalko, Lei Zhang,
On an evolution equation in a cell motility model,
Physica D: Nonlinear Phenom., 318–319, 12–25, 2016.
DOI ·
arXiv:1506.03945
[14]Christoph Ortner, Lei Zhang,
Atomistic/continuum blending with ghost force correction,
SIAM J. Sci. Comput., 38(1), A346–A375, 2016.
DOI ·
arXiv:1407.0053
[13]Li Zhang, Yao Shen, Lei Zhang, et al.,
Competing effects of interface anisotropy and isotropic driving force on the growth of steady-state shape in phase-field modeling,
Comput. Mater. Sci., 111, 313–321, 2016.
DOI
[12]Rui Du, Lei Zhang,
Domain decomposition preconditioner using rough polyharmonic splines,
Chinese Ann. Math. Ser. B, 36(5), 803–812, 2015 (special issue for the Proceedings of the Shanghai Conference in honor of Professor Luc Tartar).
DOI
[11]Christoph Ortner, Lei Zhang,
Energy-based atomistic-to-continuum coupling without ghost forces,
Comput. Methods Appl. Mech. Engrg., 279(1), 29–45, 2014.
DOI ·
arXiv:1312.6814
[10]Christoph Ortner, Alexander Shapeev, Lei Zhang,
(In-)Stability and stabilisation of QNL-type atomistic-to-continuum coupling methods,
Multiscale Model. Simul., 12(3), 1258–1293, 2014.
DOI ·
arXiv:1308.3894
[9]Houman Owhadi, Lei Zhang, Leonid Berlyand,
Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization,
ESAIM Math. Model. Numer. Anal., 48(2), 517–552, 2014.
DOI ·
arXiv:1212.0812
[8]Christoph Ortner, Lei Zhang,
Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2D model problem,
SIAM J. Numer. Anal., 50(6), 2940–2965, 2012.
DOI ·
arXiv:1110.0168
[7]Houman Owhadi, Lei Zhang,
Localized bases for finite dimensional homogenization approximations with non-separated scales and high-contrast,
Multiscale Model. Simul., 9(4), 1373–1398, 2011.
DOI ·
arXiv:1011.0986
[6]Lei Zhang, Leonid Berlyand, Maxim V. Fedorov, Houman Owhadi,
Global energy matching method for atomistic to continuum modeling of self-assembling biopolymer aggregates,
Multiscale Model. Simul., 8(5), 1958–1980, 2010.
DOI
[5]Houman Owhadi, Lei Zhang,
Numerical homogenization of the acoustic wave equations with a continuum of scales,
Comput. Methods Appl. Mech. Engrg., 198(3–4), 397–406, 2008.
DOI ·
arXiv:math/0604380
[4]Houman Owhadi, Lei Zhang,
Homogenization of parabolic equations with a continuum of space and time scales,
SIAM J. Numer. Anal., 46(1), 1–36, 2007.
DOI ·
arXiv:math/0512504
[3]Houman Owhadi, Lei Zhang,
Metric based upscaling,
Comm. Pure Appl. Math., 60(5), 675–723, 2007.
DOI ·
arXiv:math/0505223
[2]张镭, 袁礼,
Ghost Fluid 方法与双介质可压缩流动计算,
计算物理, 20(6), 503–508, 2003.
PDF
[1]张镭, 袁礼,
用改进的耦合型 Level Set 方法计算一维双介质可压缩流动,
计算物理, 18(6), 511–516, 2001.
PDF
Students & Postdocs
Postdocs
Yachen Hong (PhD, East China Normal University), 2026–present
Mingjie Liao (PhD, University of Science and Technology Beijing), 2019–2021; researcher at AsiaInfo Technologies Limited, Beijing
Peng Zhang (PhD, Paris 12), 2015–2017; researcher at the Systems Engineering Research Institute, Beijing
Xinliang Liu, 2017–2021; postdoc at King Abdullah University of Science and Technology
Yangshuai Wang, 2016–2021 (National Scholarship 2020); postdoc at University of British Columbia
Lidong Fang, 2014–2020; postdoc at Michigan State University
Haolei Wang, 2013–2020; engineer at China Electronics Technology Group Corporation
Mingjie Liao, University of Science and Technology Beijing, 2013–2019, co-supervised with Prof. Ping Lin
Matthew S. Mizuhara, Penn State University, 2012–2017, co-supervised with Prof. Leonid Berlyand; tenure-track assistant professor at The College of New Jersey
Master & Undergraduate
Master: 1 current (Yuelin Wu) and 11 graduated students.
Undergraduate: supervised 10+ undergraduate research projects and bachelor theses, including Diyi Liu (VURP at Caltech, now PhD at Minnesota), Dongping Qi (now PhD at Cornell), and Keyu Zhu (now PhD at Georgia Tech).
Organization
Minisymposium “Multiscale Finite Element Method”, 11th Finite Element Conference, Chongqing, Sep 2023
Minisymposium “Mathematical modeling and numerical analysis for multiscale methods”, CMAM 2022, Vienna, Sep 2022
Workshop on Computational Mathematics and Mechanics, University of Science and Technology Beijing, Jul 2021
2018 International Graduate Summer School on “Frontiers of Applied and Computational Mathematics” (with Shi Jin et al.), Shanghai Jiao Tong University, Jul 2018