• Submitted and Preprint

Amplitude Expansion Phase Field Crystal (APFC) Modeling based Efficient Dislocation Simulations using Fourier Pseudospectral Method. Xinyi Wei, Yangshuai Wang, Kai Jiang, Lei Zhang, submitted, 2024. Preprint.

An Adaptive Angular Domain Compression Scheme For Solving Multiscale Radiative Transfer Equation. Qinchen Song, Jingyi Fu, Min Tang, Lei Zhang, submitted, 2024. Preprint.

Dilated convolution neural operator for multiscale partial differential equations. Bo Xu, Xinliang Liu, Lei Zhang, submitted, 2024. Preprint.

Projection method for quasiperiodic elliptic equations and application to quasiperiodic homogenization. Kai Jiang, Meng Li, Juan Zhang, Lei Zhang, submitted, 2024. Preprint.

Quantum circuits for partial differential equations via Schrödingerisation. Junpeng Hu, Shi Jin, Nana Liu, Lei Zhang, submitted, 2024. Preprint.

MeshAC: A 3D mesh generation and adaptation package for multiscale coupling methods. Kejie Fu, Mingjie Liao, Yangshuai Wang, Jianjun Chen, Lei Zhang, submitted, 2024. Preprint.

Dilation theorem via Schrödingerisation, with applications to the quantum simulation of differential equations. Junpeng Hu, Shi Jin, Nana Liu, Lei Zhang, submitted, 2023. Preprint.

Higher order far-field boundary conditions for crystalline defects. Julian Braun, Christoph Ortner, Yangshuai Wang, Lei Zhang, submitted, 2022. Preprint.




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• Publications

A Comprehensive Deep Learning–Based Approach to Field Reconstruction in Reactor Cores. Bo Xu, Han Li, Lei Zhang, Helin Gong, Nucl. Sci. Eng., accepted, 2024.

Enhancing accuracy in deep learning using random matrix theory. Leonid Berlyand, Etienne Sandier, Yitzchak Shmalo, Lei Zhang, J. Mach. Learn., accepted, 2024. Preprint.

Slip-discreteness-corrected strain gradient crystal plasticity (SDC-SGCP) theory. Ran Chen, Guisen Liu, Peidong Wu, Jian Wang, Lei Zhang, Yao Shen, Int. J. Plast., 180, 104054, 2024.

DNA-SE: Towards Deep Neural-Nets Assisted Semiparametric Estimation. Qinshuo Liu, Zixin Wang, Xi-An Li, Xinyao Ji, Lei Zhang, Lin Liu, and Zhonghua Liu, ICML, accepted, 2024. Preprint.

A posteriori error estimate and adaptivity for QM/MM models of crystalline defects. Yangshuai Wang, James R. Kermode, Christoph Ortner, Lei Zhang, Comput. Methods Appl. Mech. Engrg., 428, 117097, 2024. Preprint.

Quantum algorithms for multiscale partial differential equations. Junpeng Hu, Shi Jin, Lei Zhang, Multiscale Model. Simul., accepted, 2024. Preprint.

Mitigating spectral bias for the multiscale operator learning with hierarchical attention. Xinliang Liu, Bo Xu, Lei Zhang, J. Comput. Phys., 506, 112944, 2024. Preprint.

Elastic far-field decay from dislocations in multilattices. Dereck Olson, Chirstoph Ortner, Yangshuai Wang, Lei Zhang, Multiscale Model. & Simul., 21(4), 1379-1409, 2023. Preprint.

A fast front-tracking approach and its analysis for a temporal multiscale flow problem with a fractional-order boundary growth based non-Newtonian hydrodynamic model. Zhaoyang Wang, Ping Lin, Lei Zhang, SIAM J. Sci. Comput., 45(5), B646-B672, 2023. Preprint.

Subspace decomposition based DNN algorithm for elliptic-type multi-scale PDEs. Xi-An Li, Zhi-Qin John Xu, Lei Zhang, J. Comput. Phys., 488, 112242, 2023. Preprint.

Adaptive multigrid strategy for large-scale molecular mechanics optimization. Mingjie Liao, Yangshuai Wang, Kejie Fu, Jianjun Chen, Lei Zhang, J. Comput. Phys., 485, 112113, 2023. Preprint.

On multilevel Monte Carlo methods for deterministic and uncertain hyperbolic systems. Junpeng Hu, Shi Jin, Jinglai Li, Lei Zhang, submitted, 2022. J. Comput. Phys., 475, 111847, 2023. Preprint.

Optimal control for multiscale PDEs with rough coefficients. Yanping Chen, Xinliang Liu, Lei Zhang, Jiaoyan Zeng, J. Comput. Math., 41, 842-866, 2023. Preprint.

DeePN2: A deep learning-based non-Newtonian hydrodynamic model. Lidong Fang, Pei Ge, Lei Zhang, Huan Lei, Weinan E, J. Mach. Learn., 1, 114-140, 2022. Preprint.

On the multiscale Landau-Lifshitz-Gilbert equation: Two-scale convergence and stability analysis. Jingrun Chen, Rui Du, Zetao Ma, Zhiwei Sun, Lei Zhang, Multiscale Model. Simul., 20(2), 835-856, 2022.

Generalized rough polyharmonic splines for multiscale PDEs with rough coefficients. Xinliang Liu, Lei Zhang, Shengxin Zhu, Numer. Math. Theor. Meth. Appl., 14, 862-892, 2021. Preprint.

Iterated numerical homogenization for multi-scale elliptic equations with monotone nonlinearity. Xinliang Liu, Eric Chung, Lei Zhang, Multiscale Model. Simul., 19(4), 1601–1632, 2021. Preprint.

A posteriori error estimates for adaptive QM/MM coupling methods. Yangshuai Wang, Huajie Chen, Mingjie Liao, Christoph Ortner, Hao Wang, Lei Zhang, SIAM J. Sci. Comput., 43(4), A2785–A2808, 2021. Preprint.

Blended ghost force correction method for 3d crystalline defects. Lidong Fang, Lei Zhang, Commun. Comput. Phys., 29, 1246-1272, 2021. Preprint.

A priori analysis of a higher order nonlinear elasticity model for an atomistic chain with periodic boundary condition. Yangshuai Wang, Hao Wang, Lei Zhang, IMA J. Num. Anal., 41(2), 1465-1495, 2021. Preprint.

A DNN-based algorithm for multi-scale elliptic problems. Xi'an Li, Zhiqin John Xu, Lei Zhang, Commun. Comput. Phys., 1886-1906, special issue on "Machine learning for scientific computing", 2020. Preprint.

Surface anchoring controls orientation of a microswimmer in nematic liquid crystal. Hai Chi, Mikhailo Potomkin, Lei Zhang, Igor Aronson, Leonid Berlyand, Commun. Phys., 3, Article 162, 2020.

Energy minimization and preconditioning in the simulation of athermal granular materials in two dimensions. Haolei Wang, Lei Zhang, Electron. Res. Arch., 28(1), 405-421, 2020. Preprint.

Surface, size and topological effects for some nematic equilibria on rectangular domains. Lidong Fang, Apala Majumdar, Lei Zhang, Math. Mech. Solid, 25(5), 1101-1123, 2020. Preprint.

A posteriori error estimate and adaptive mesh refinement algorithm for atomistic/continuum coupling with finite range interactions in two dimensions. Mingjie Liao, Ping Lin, Lei Zhang, Commun. Comput. Phys., 27, 198-226, 2020. Preprint.

Fast eigenpairs computation with operator adapted wavelets and hierarchical subspace correction. Hehu Xie, Lei Zhang, Houman Owhadi, SIAM J. Num. Anal. 57(6), 2519-2550, 2019. Preprint.

Adaptive QM/MM coupling for crystalline defects. Huajie Chen, Mingjie Liao, Hao Wang, Yangshuai Wang, Lei Zhang, Comput. Methods Appl. Mech. Engrg., 354, 351-368, 2019. Preprint.

Optimizing parallel section length for small tensile specimen with fabrication non-uniformity in thickness. Haiting Liu, Ran Chen, Mao Wen, Lei Zhang, Yao Shen, Fusion Eng. Des., 147, 111244, 2019. Preprint.

A posteriori error estimation and adaptive algorithm for the atomistic/continuum coupling in 2D. Hao Wang, Mingjie Liao, Ping Lin, Lei Zhang, SIAM J. Sci. Comput., 40(4), A2087–A2119, 2018. Preprint.

Experimental studies of vibrational modes in a two-dimensional amorphous solid. Ling Zhang, Jie Zheng, Yinqiao Wang, Lei Zhang, Zhaohui Jin, Liang Hong, Yujie Wang, Jie Zhang, Nature Commun., 8, Article 67, 2017.

Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients. Houman Owhadi, Lei Zhang, J. Comput. Phys., 347, 99-128, 2017. Preprint.

A comprehensive solution to miniaturized tensile testing: Specimen geometry optimization and extraction of constitutive behaviors using inverse FEM procedure. Haiting Liu, Yao Sheng, Shuang Yang, Pengfei Zheng, Lei Zhang, Fusion Eng. Des., 121, 188-197, 2017.

Atomistic/continuum blending with ghost force correction. Christoph Ortner, Lei Zhang, SIAM J. Sci. Comput., 38(1), A346-A375, 2016. Preprint.

Effects of interface anisotropy and isotropic driving force on the growth of steady-state shape in phase-field modeling. Li Zhang, Yao Shen, Lei Zhang, et. al., Comput. Mat. Sci., 111, 313-321, 2016.

On an evolution equation in a cell motility model. Matthew S. Mizuhara, Leonid Berlyand, Volodymyr Rybalko, Lei Zhang, Physica D: Nonlinear phenom., 318-319, 12-25, 2016. Preprint.

Domain decomposition preconditioner using rough polyharmonic splines. Rui Du, Lei Zhang, Chinese Ann. Math. Ser. B, 36(5), 803-812, as Procccedings of the Shanghai Conference in honor of Professor Luc Tartar, 2015.

Energy-based atomistic-to-continuum coupling without ghost forces. C. Ortner, L. Zhang , Comput. Methods Appl. Mech. Engrg., 279 (1), 29-45, 2014. Preprint.

(In-)stability and stabilisation of QNL-Type atomistic-to-continuum coupling methods. C. Ortner, A. Shapeev, L. Zhang , Multiscale Model. Simul., 12 (3), 1258-1293, 2014. Preprint.

Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization. H. Owhadi, L. Zhang, L. Berlyand , ESAIM Math. Model. Numer. Anal. (M2AN), 48:2, 517-552, 2014. Preprint.

Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2D model problem. C. Ortner, L. Zhang , SIAM J. Numer. Anal., Volume 50, Issue 6, pp. 2940-2965, 2012. Preprint.

Localized bases for finite dimensional homogenization approximations with non-separated scales and high-contrast. H. Owhadi, L. Zhang , Multiscale Model. Simul., Volume 9, Issue 4, pp. 1373-1398, 2011. Preprint.

Global energy matching method for atomistic-to-continuum modeling of self-assembling biopolymer aggregates. L. Zhang, L. Berlyand, M. V. Fedorov, and H. Owhadi , Multiscale Model. Simul., Volume 8, Issue 5, pp. 1958-1980, 2010. Preprint.

Numerical homogenization of the accoustic wave equation with a continuum scales. H. Owhadi, L. Zhang , Comput. Methods Appl. Mech. Engrg., Volume 198, Issues 3-4, Pages 397-406, Dec 15 2008. Preprint.

Homogenization of parabolic equations with a continuum space and time scales. H. Owhadi, L. Zhang , SIAM J. Numer. Anal., Volume 46, Issue 1, pp. 1-36, 2007. Preprint. Movies (YouTube): u in euclidean coordinates, u in caloric coordinates, gradient of u in Euclidean coordinates, gradient of u in caloric cooridinates, image of fine mesh in caloric coordinates.

Metric based upscaling. H. Owhadi, L. Zhang , Commun. Pure Appl. Math., Vol. 60, Issue 5, p 675-723, 2007. Preprint.

Ghost Fluid方法与双介质可压缩流动计算. 张镭，袁礼, 计算物理, 20, 6, 503-508, 2003.

用改进的耦合型Level Set方法计算一维双介质可压缩流动. 张镭, 袁礼, 计算物理, 18, 6, 511-516, 2001.

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• PhD & Postdocs

Xiaozhe Zheng, PhD, 2023-now.

Tailong Jin, PhD, 2022-now.

Xinyi Wei, PhD, 2021-now.

Zetao Mao, PhD, 2021-now.

Bo Xu, PhD, 2020-now.

Qinchen Song, PhD, 2020-now.

Junpeng Hu, PhD, 2020-now, co-supervised with Prof. Shi Jin.

Mingjie Liao, Postdoc, 2019-2021, currently researcher at AsiaInfo Technologies Limited, Beijing.

Xi'an Li, PhD, 2018-2022.

Xingliang Liu, PhD, 2017-2021, postdoc at KAUST, Saudi Arabia, with Prof. Jinchao Xu.

Yangshuai Wang, PhD, 2016-2021, postdoc at UBC, Canada, with Prof. Christoph Ortner.

Peng Zhang, Postdoc (PhD Paris 12), 2015-2017, currently researcher at the Systems Engineering Research Institute, Beijing..

Lidong Fang, PhD, 2014-2020, postdoc at MSU, USA, with Prof. Huan Lei.

Haolei Wang, PhD, 2013-2020, engineer at China Electronics Technology Group Corporation.

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• Organizations



International Workshop on Mathematical Theory, Methods and Application in Materials Simulation at Shanghai Jiao Tong University, Apr 9-11, 2021

Multiscale Problems in Materials Science and Biology: Analysis and Computation at Tsinghua Sanya International Mathematics Forum (TSIMF), Jan 8-12, 2018

Short Course on Tensor Numerical Methods for Multidimensional PDEs, Apr. 06 - Apr. 12, 2017. Lectures 7-9, Lectures 10-11, Lectures 12, Lectures 13-14, Lectures 15, Matlab Exercises.

Workshop on Multiscale Modeling and Analysis in Materials Science -- A Satellite Meeting of ICIAM 2015, Aug 6-8, 2015

Workshop on Multiscale Problems from Physics, Biology and Materials Science, May 28-31, 2014

Workshop on Multiscale Modeling and Simulation in Materials Science, Apr 21-23, 2013

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• Grants

NSFC grant 12271360, PI, 2023-2026.

Shanghai Science and Technology Committee, PI, 2022-2025.

Shanghai Science and Technology Committee, co-PI, 2021-2023.

NSFC-DFG joint grant 11861131004, co-PI, 2019-2021.

NSFC grant 11871339, PI, 2019-2022.

NSFC grant 11571314, co-PI, 2016-2019.

Intel Higher Education research fund, PI, 2015-2016.

NSFC grant 11471214 (Construction, Analysis and Applications of Two Classes of Typical Multiscale Methods), PI, 2015-2018.

Research Facilitation.

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