Homogenization of Parabolic Equations with a Continuum of Space and Time Scales. - Houman Owhadi; Lei Zhang 027 (SIAM J. Numer. Anal., 2007)

Global Energy Matching Method for Atomistic-to-Continuum Modeling of Self-Assembling Biopolymer Aggregates. - Lei Zhang 027; Leonid Berlyand; Maxim V. Fedorov; Houman Owhadi (Multiscale Model. Simul., 2010)

Localized Bases for Finite-Dimensional Homogenization Approximations with Nonseparated Scales and High Contrast. - Houman Owhadi; Lei Zhang 027 (Multiscale Model. Simul., 2011)

Construction and Sharp Consistency Estimates for Atomistic/Continuum Coupling Methods with General Interfaces: A Two-Dimensional Model Problem. - Christoph Ortner; Lei Zhang 027 (SIAM J. Numer. Anal., 2012)

(In-)stability and Stabilization of QNL-Type Atomistic-to-Continuum Coupling Methods. - Christoph Ortner; Alexander V. Shapeev; Lei Zhang 027 (Multiscale Model. Simul., 2014)

Atomistic/Continuum Blending with Ghost Force Correction. - Christoph Ortner; Lei Zhang 027 (SIAM J. Sci. Comput., 2016)

Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients. - Houman Owhadi; Lei Zhang 027 (J. Comput. Phys., 2017)

A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions. - Hao Wang 051; Mingjie Liao; Ping Lin; Lei Zhang 027 (SIAM J. Sci. Comput., 2018)

Energy Minimization and Preconditioning in the Simulation of Athermal Granular Materials in Two Dimensions. - Haolei Wang; Lei Zhang 027 (CoRR, 2019)

Fast Eigenpairs Computation with Operator Adapted Wavelets and Hierarchical Subspace Correction. - Hehu Xie; Lei Zhang 027; Houman Owhadi (SIAM J. Numer. Anal., 2019)

Curvature Estimation on Point Cloud Using an Indicator Function. - Maolin Tian; Jian Lu; Lei Zhang 027 (HPCCT/BDAI, 2020)

Iterated numerical homogenization for multi-scale elliptic equations with monotone nonlinearity. - Xinliang Liu; Eric Tsz Shun Chung; Lei Zhang 027 (CoRR, 2021)

Generalized Rough Polyharmonic Splines for Multiscale PDEs with Rough Coefficients. - Xinliang Liu; Lei Zhang 027; Shengxin Zhu (CoRR, 2021)

Iterated Numerical Homogenization for MultiScale Elliptic Equations with Monotone Nonlinearity. - Xinliang Liu; Eric Tsz Shun Chung; Lei Zhang 027 (Multiscale Model. Simul., 2021)

A Posteriori Error Estimates for Adaptive QM/MM Coupling Methods. - Yangshuai Wang; Huajie Chen; Mingjie Liao; Christoph Ortner; Hao Wang 051; Lei Zhang 027 (SIAM J. Sci. Comput., 2021)

A Posteriori Error Estimate and Adaptivity for QM/MM Models of Crystalline Defects. - Yangshuai Wang; James R. Kermode; Christoph Ortner; Lei Zhang 027 (CoRR, 2022)

HT-Net: Hierarchical Transformer based Operator Learning Model for Multiscale PDEs. - Xinliang Liu; Bo Xu; Lei Zhang 027 (CoRR, 2022)

On the Multiscale Landau-Lifshitz-Gilbert Equation: Two-Scale Convergence and Stability Analysis. - Jingrun Chen; Rui Du; Zetao Ma; Zhiwei Sun; Lei Zhang 027 (Multiscale Model. Simul., 2022)

Enhancing Accuracy in Deep Learning Using Random Matrix Theory. - Leonid Berlyand; Etienne Sandier; Yitzchak Shmalo; Lei Zhang 027 (CoRR, 2023)

Adaptive multigrid strategy for geometry optimization of large-scale three dimensional molecular mechanics. - Kejie Fu; Mingjie Liao; Yangshuai Wang; Jianjun Chen 002; Lei Zhang 027 (J. Comput. Phys., 2023)

A Fast Front-Tracking Approach and Its Analysis for a Temporal Multiscale Flow Problem with a Fractional Order Boundary Growth. - Zhaoyang Wang 005; Ping Lin; Lei Zhang 027 (SIAM J. Sci. Comput., 2023)

Elastic Far-Field Decay from Dislocations in Multilattices. - Derek Olson; Christoph Ortner; Yangshuai Wang; Lei Zhang 027 (Multiscale Model. Simul., 2023)

Mitigating spectral bias for the multiscale operator learning. - Xinliang Liu; Bo Xu; Shuhao Cao; Lei Zhang 027 (J. Comput. Phys., 2024)

Quantum Algorithms for Multiscale Partial Differential Equations. - Junpeng Hu; Shi Jin; Lei Zhang 027 (Multiscale Model. Simul., 2024)

MeshAC: A 3D mesh generation and adaptation package for multiscale coupling methods. - Kejie Fu; Mingjie Liao; Yangshuai Wang; Jianjun Chen 002; Lei Zhang 027 (Comput. Phys. Commun., 2025)

Dilated convolution neural operator for multiscale partial differential equations. - Bo Xu; Xinliang Liu; Lei Zhang 027 (J. Comput. Appl. Math., 2025)

Higher-Order Far-Field Boundary Conditions for Crystalline Defects. - Julian Braun; Christoph Ortner; Yangshuai Wang; Lei Zhang 027 (SIAM J. Numer. Anal., 2025)

Numerical Homogenization of Landau-Lifshitz Equation with Rough Coefficients. - Zetao Ma; Jingrun Chen; Rui Du; Lei Zhang 027 (CoRR, 2025)

An Adaptive Angular Domain Compression Scheme For Solving Multiscale Radiative Transfer Equations. - Qinchen Song; Jingyi Fu; Min Tang; Lei Zhang 027 (J. Sci. Comput., 2025)