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E, Weinan

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Author ID: e.weinan Recent zbMATH articles by "E, Weinan"
Published as: E, W.; E, Weinan; E., Weinan; Veinan, I.; Weinan, E; Weinan, E.; É, Weinan
Homepage: https://web.math.princeton.edu/~weinan/
External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND
Documents Indexed: 178 Publications since 1984, including 4 Books
all top 5

Co-Authors

19 single-authored
20 Lu, Jianfeng
20 Vanden-Eijnden, Eric
11 Liu, Jianguo
11 Ren, Weiqing
9 Engquist, Bjorn E.
7 Li, Tiejun
7 Lin, Lin
7 Shu, Chi-Wang
7 Zhang, Pingwen
6 Li, Xiantao
6 Ma, Chao
6 Ying, Lexing
5 Han, Jiequn
5 Jentzen, Arnulf
5 Li, Qianxiao
5 Ming, Pingbing
5 Sinaĭ, Yakov Grigor’evich
4 García-Cervera, Carlos J.
4 Zhou, Xiang
3 Abdulle, Assyr
3 Liu, Di
3 Shen, Hao
3 Tai, Cheng
3 Yue, Xingye
2 Avellaneda, Marco
2 Chen, Shanqin
2 Cheng, Xiuyuan
2 Huang, Hongci
2 Li, Dong
2 Mattingly, Jonathan C.
2 Palffy-Muhoray, Peter
2 Rykov, Yurii G.
2 Wan, Xiaoliang
2 Wang, Qingcan
2 Wang, Xiaoping
2 Wu, Lei
2 Wu, Lei
2 Yang, Chao
2 Yang, Xu
2 Yip, Nung Kwan
1 Bai, Zhaojun
1 Beck, Christian
1 Caffarelli, Luis Ángel
1 Cai, Zhiqiang
1 Car, Roberto
1 Chan, Tony Fan-Cheong
1 Chazelle, Bernard
1 Chen, Long
1 Chen, Shiyi
1 Chen, Zhengting
1 Chen, Zhiming
1 Cheng, Li-Tien
1 Constantin, Peter
1 Dai, Yu-Hong
1 Friesecke, Gero
1 Gao, Weiguo
1 Gimbutas, Zydrunas
1 Han, Weimin
1 Hou, Thomas Yizhao
1 Hu, Dan
1 Huang, Zhongyi
1 Hutzenthaler, Martin
1 Khanin, Konstantin M.
1 Kohn, Robert Vita
1 Kruse, Thomas
1 Lin, Ling
1 Liu, Yunxian
1 Ma, Zheng
1 Mazel, Alexander E.
1 Meza, Juan C.
1 Mu, Mo
1 Muratov, Cyrill B.
1 Nie, Xiaobo
1 Otto, Felix
1 Pettifor, David
1 Robbins, Mark O.
1 Ryan, Reade
1 Samanta, Amit
1 Schulze, Tim P.
1 Serre, Denis
1 Shao, Sihong
1 Shi, An-Chang
1 Smereka, Peter
1 Sun, Jiachang
1 Sun, Yi
1 Titi, Edriss Saleh
1 Trinh, Philippe H.
1 Wang, Chu
1 Wang, Jianchun
1 Wang, Ke
1 Wang, Xiao-Ping
1 Wang, Yao
1 Wehr, Jan
1 Wojtowytsch, Stephan
1 Xin, Jack X.
1 Yang, Huanan
1 Yang, Jerry Zhijian
1 Yao, Yuan
1 Yu, Bing
1 Yu, Haijun
...and 1 more Co-Authors
all top 5

Serials

22 Journal of Computational Physics
13 Communications on Pure and Applied Mathematics
13 Communications in Mathematical Sciences
7 Physics of Fluids
6 Communications in Mathematical Physics
6 Journal of Statistical Physics
6 Science China. Mathematics
5 SIAM Journal on Numerical Analysis
5 Proceedings of the National Academy of Sciences of the United States of America
5 Communications in Computational Physics
4 Nonlinearity
4 Journal of Computational Mathematics
4 Physica D
3 Archive for Rational Mechanics and Analysis
3 Acta Mathematicae Applicatae Sinica. English Series
3 Methods and Applications of Analysis
3 Discrete and Continuous Dynamical Systems
3 Journal of Machine Learning Research (JMLR)
3 Communications in Mathematics and Statistics
3 Research in the Mathematical Sciences
2 Journal of Fluid Mechanics
2 Russian Mathematical Surveys
2 Mathematics of Computation
2 Chinese Annals of Mathematics. Series B
2 Notices of the American Mathematical Society
2 Journal of Nonlinear Science
2 Acta Mathematica Sinica. English Series
1 International Journal for Numerical Methods in Fluids
1 Journal of Mathematical Physics
1 Journal of the Mechanics and Physics of Solids
1 Physics of Fluids, A
1 ACM Transactions on Mathematical Software
1 Memoirs of the American Mathematical Society
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Studies in Applied Mathematics
1 Mathematica Numerica Sinica
1 Applied Numerical Mathematics
1 Communications in Applied Numerical Methods
1 Journal of the American Mathematical Society
1 Asymptotic Analysis
1 Journal of Scientific Computing
1 Communications in Partial Differential Equations
1 Journal of Non-Newtonian Fluid Mechanics
1 SIAM Journal on Applied Mathematics
1 SIAM Journal on Scientific Computing
1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings
1 Annals of Mathematics. Second Series
1 Discrete and Continuous Dynamical Systems. Series B
1 Physical Review E. Third Series
1 Multiscale Modeling & Simulation
1 Acta Numerica
1 Oberwolfach Reports
1 Graduate Studies in Mathematics
1 IAS/Park City Mathematics Series
1 The Journal of Chemical Physics
1 Pure and Applied Functional Analysis

Publications by Year

Citations contained in zbMATH Open

154 Publications have been cited 3,585 times in 2,541 Documents Cited by Year
The heterogeneous multiscale methods. Zbl 1093.35012
E, Weinan; Engquist, Bjorn
320
2003
Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics. Zbl 0852.35097
E, Weinan; Rykov, Yu. G.; Sinai, Ya. G.
144
1996
Onsager’s conjecture on the energy conservation for solutions of Euler’s equation. Zbl 0818.35085
Constantin, Peter; E, Weinan; Titi, Edriss S.
144
1994
Heterogeneous multiscale methods: a review. Zbl 1164.65496
E, Weinan; Engquist, Bjorn; Li, Xiantao; Ren, Weiqing; Vanden-Eijnden, Eric
138
2007
The heterogeneous multiscale method. Zbl 1255.65224
Abdulle, Assyr; Weinan, E.; Engquist, Björn; Vanden-Eijnden, Eric
113
2012
Invariant measures for Burgers equation with stochastic forcing. Zbl 0972.35196
E, Weinan; Khanin, K.; Mazel, A.; Sinai, Ya.
99
2000
Analysis of the heterogeneous multiscale method for elliptic homogenization problems. Zbl 1060.65118
E, Weinan; Ming, Pingbing; Zhang, Pingwen
90
2005
Blowup of solutions of the unsteady Prandtl’s equation. Zbl 0908.35099
E, Weinan; Engquist, Bjorn
86
1997
Minimum action method for the study of rare events. Zbl 1050.60068
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
81
2004
Projection method. I: Convergence and numerical boundary layers. Zbl 0842.76052
E, Weinan; Liu, Jian-Guo
75
1995
Boundary layer theory and the zero-viscosity limit of the Navier-Stokes equation. Zbl 0961.35101
E, Weinan
74
2000
Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation. Zbl 0994.60065
E, Weinan; Mattingly, J. C.; Sinai, Ya.
65
2001
Vorticity boundary condition and related isssues for finite difference schemes. Zbl 0847.76050
E, Weinan; Liu, Jian-Guo
64
1996
Small-scale structures in Boussinesq convection. Zbl 0822.76087
E, Weinan; Shu, Chi-Wang
62
1994
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Zbl 1382.65016
E, Weinan; Han, Jiequn; Jentzen, Arnulf
58
2017
Cauchy-Born rule and the stability of crystalline solids: Static problems. Zbl 1106.74019
E, Weinan; Ming, Pingbing
58
2007
Principles of multiscale modeling. Zbl 1238.00010
E, Weinan
57
2011
Essentially compact schemes for unsteady viscous incompressible flows. Zbl 0853.76045
E, Weinan; Liu, Jian-Guo
55
1996
Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity. Zbl 0814.34039
E, Weinan
54
1994
Homogenization of linear and nonlinear transport equations. Zbl 0794.35014
E, Weinan
45
1992
Gauge method for viscous incompressible flows. Zbl 1160.76329
E, Weinan; Liu, Jian-Guo
44
2003
Analysis of multiscale methods for stochastic differential equations. Zbl 1080.60060
E, Weinan; Liu, Di; Vanden-Eijnden, Eric
43
2005
Solving high-dimensional partial differential equations using deep learning. Zbl 1416.35137
Han, Jiequn; Jentzen, Arnulf; E, Weinan
42
2018
Numerical methods for the Landau–Lifshitz equation. Zbl 0988.65079
E, Weinan; Wang, Xiao-Ping
41
2000
A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow. Zbl 1059.76060
Nie, X. B.; Chen, S. Y.; E, Weinan; Robbins, M. O.
40
2004
Multiscale modeling and computation. Zbl 1032.65013
E, Weinan; Engquist, Bjorn
39
2003
Ergodicity for the Navier-Stokes equation with degenerate random forcing: finite-dimensional approximation. Zbl 1024.76012
E, Weinan; Mattingly, Jonathan C.
39
2001
Well-posedness for the dumbbell model of polymeric fluids. Zbl 1060.35169
E, Weinan; Li, Tiejun; Zhang, Pingwen
38
2004
A dynamic atomistic–continuum method for the simulation of crystalline materials. Zbl 1013.82022
E, Weinan; Huang, Zhongyi
36
2002
Finite difference heterogeneous multi-scale method for homogenization problems. Zbl 1034.65067
Abdulle, Assyr; E, Weinan
35
2003
The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems. Zbl 1392.35306
E, Weinan; Yu, Bing
33
2018
Multiscale modeling of the dynamics of solids at finite temperature. Zbl 1120.74313
Li, Xiantao; E, Weinan
33
2005
On the crystallization of 2D hexagonal lattices. Zbl 1180.82191
E, Weinan; Li, Dong
32
2009
Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales. Zbl 1162.80003
E, Weinan; Liu, Di; Vanden-Eijnden, Eric
31
2007
Towards a theory of transition paths. Zbl 1101.82016
E, Weinan; Vanden-Eijnden, Eric
31
2006
Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics. Zbl 1143.76541
Ren, Weiqing; E, Weinan
30
2005
Analysis of the heterogeneous multiscale method for ordinary differential equations. Zbl 1088.65552
E, Weinan
29
2003
The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size. Zbl 1158.74541
Yue, Xingye; E, Weinan
28
2007
Boundary conditions for the moving contact line problem. Zbl 1146.76513
Ren, Weiqing; E, Weinan
26
2007
A Gauss-Seidel projection method for micromagnetics simulations. Zbl 1012.82002
Wang, Xiao-Ping; García-Cervera, Carlos J.; E, Weinan
26
2001
Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems. Zbl 1182.65072
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Car, Roberto; E, Weinan
25
2009
Statistical properties of shocks in Burgers turbulence. Zbl 0844.35144
Avellaneda, Marco; E, Weinan
25
1995
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework. I: Total energy calculation. Zbl 1251.82008
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
23
2012
A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow. Zbl 0790.76055
E, Weinan; Shu, Chi-Wang
22
1994
Aubry-Mather theory and periodic solutions of the forced Burgers equation. Zbl 0916.35099
E, Weinan
21
1999
Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on nonstaggered grids. Zbl 0901.76046
E, Weinan; Liu, Jian-Guo
20
1997
Projection method. II: Godunov-Ryabenki analysis. Zbl 0920.76056
E, Weinan; Liu, Jian-Guo
20
1996
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. Zbl 1442.91116
Beck, Christian; E, Weinan; Jentzen, Arnulf
19
2019
A proposal on machine learning via dynamical systems. Zbl 1380.37154
E, Weinan
19
2017
Continuum models for the contact line problem. Zbl 1308.76082
Ren, Weiqing; Hu, Dan; Weinan, E.
19
2010
Variational boundary conditions for molecular dynamics simulations of solids at low temperature. Zbl 1114.74326
Li, Xiantao; E, Weinan
19
2006
The heterogeneous multi-scale method for homogenization problems. Zbl 1086.65521
E, Weinan; Engquist, Björn
19
2005
Some recent progress in multiscale modeling. Zbl 1419.74252
E, Weinan; Li, Xiantao; Vanden-Eijnden, Eric
19
2004
The gentlest ascent dynamics. Zbl 1237.37052
E, Weinan; Zhou, Xiang
18
2011
SelInv – an algorithm for selected inversion of a sparse symmetric matrix. Zbl 1365.65069
Lin, Lin; Yang, Chao; Meza, Juan C.; Lu, Jianfeng; Ying, Lexing; E, Weinan
17
2011
Cauchy-Born rule and the stability of crystalline solids: dynamic problems. Zbl 1138.35063
E, Weinan; Ming, Pingbing
17
2007
Generalized flows, intrinsic stochasticity, and turbulent transport. Zbl 0967.76038
E, Weinan; Vanden Eijnden, Eric
17
2000
Nonlinear continuum theory of smectic-\(A\) liquid crystals. Zbl 0891.76009
E, Weinan
17
1997
The initial-value problem for measure-valued solutions of a canonical \(2 \times 2\) system with linearly degenerate fields. Zbl 0784.35059
E, Weinan; Kohn, Robert V.
16
1991
The electronic structure of smoothly deformed crystals: Wannier functions and the Cauchy-Born Rule. Zbl 1253.74025
E, Weinan; Lu, Jianfeng
15
2011
Study of the noise-induced transition and the exploration of the phase space for the Kuramoto-Sivashinsky equation using the minimum action method. Zbl 1185.82044
Wan, X.; Zhou, X.; E, W.
15
2010
Effectiveness of implicit methods for stiff stochastic differential equations. Zbl 1199.65010
Li, Tiejun; Abdulle, Assyr; Weinan, E
15
2008
Statistical theory for the stochastic Burgers equation in the inviscid limit. Zbl 1037.76013
E, Weinan; Vanden Eijnden, Eric
15
2000
Finite difference schemes for incompressible flows in the velocity-impulse density formulation. Zbl 0870.76048
E, Weinan; Liu, Jian-Guo
15
1997
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations. Zbl 1418.65149
E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
14
2019
Continuum theory of epitaxial crystal growth. I. Zbl 1074.76504
E, Weinan; Yip, Nung Kwan
14
2001
Study of noise-induced transitions in the Lorenz system using the minimum action method. Zbl 1202.34104
Zhou, Xiang; E, Weinan
13
2010
A molecular kinetic theory of inhomogeneous liquid crystal flow and the small Deborah number limit. Zbl 1131.76010
E, Weinan; Zhang, Pingwen
13
2006
Self-induced stochastic resonance in excitable systems. Zbl 1109.34040
Muratov, Cyrill B.; Vanden-Eijnden, Eric; E, Weinan
13
2005
Large time behavior and homogenization of solutions of two-dimensional conservation laws. Zbl 0797.35114
Engquist, Bjorn; E, Weinan
13
1993
Homogenization of scalar conservation laws with oscillatory forcing terms. Zbl 0755.35068
E, Weinan
13
1992
The Kohn-Sham equation for deformed crystals. Zbl 1435.74001
E, Weinan; Lu, Jianfeng
12
2013
Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model. Zbl 1277.81117
E, Weinan; Lu, Jianfeng
12
2010
A general strategy for designing seamless multiscale methods. Zbl 1280.76038
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
12
2009
Energy landscapes and rare events. Zbl 1023.65004
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
12
2002
Projection method. III: Spatial discretization on the staggered grid. Zbl 1058.76043
E, Weinan; Liu, Jian-Guo
12
2002
Convergence of Fourier methods for the Navier-Stokes equations. Zbl 0776.76021
E, Weinan
12
1993
A class of homogenization problems in the calculus of variations. Zbl 0773.49007
E, Weinan
12
1991
Localized bases of eigensubspaces and operator compression. Zbl 1205.15017
E, Weinan; Li, Tiejun; Lu, Jianfeng
11
2010
Analysis of multiscale methods. Zbl 1046.65108
E, Weinan; Ming, Pingbing
11
2004
Convergence of spectral methods for Burgers’ equation. Zbl 0764.65057
E, Weinan
11
1992
A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. Zbl 1230.65039
Lin, Lin; Yang, Chao; Lu, Jianfeng; Ying, Lexing; E, Weinan
10
2011
Derivation of continuum models for the moving contact line problem based on thermodynamic principles. Zbl 1414.76019
Ren, Weiqing; E, Weinan
10
2011
Analysis of the local quasicontinuum method. Zbl 1188.74019
E, Weinan; Ming, Pingbing
10
2005
Metastability, conformation dynamics, and transition pathways in complex systems. Zbl 1141.82312
E, Weinan; Vanden-Eijnden, Eric
10
2004
Simple finite element method in vorticity formulation for incompressible flows. Zbl 0977.76048
Liu, Jian-Guo; E, Weinan
10
2001
Phase separation in incompressible systems. Zbl 1110.82304
E, Weinan; Palffy-Muhoray, P.
10
1997
Correctors for the homogenization of conservation laws with oscillatory forcing terms. Zbl 0766.35026
Weinan, E.; Serre, Denis
10
1992
Pole-based approximation of the Fermi-Dirac function. Zbl 1188.41007
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Weinan, E.
9
2009
Numerical methods for multiscale transport equations and application to two-phase porous media flow. Zbl 1089.76049
Yue, Xingye; E, Weinan
9
2005
Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth. Zbl 1023.82007
Schulze, Tim P.; Smereka, Peter; E, Weinan
9
2003
Gibbsian dynamics and invariant measures for stochastic dissipative PDEs. Zbl 1023.60057
E, Weinan; Liu, Di
9
2002
A mean-field optimal control formulation of deep learning. Zbl 1421.49021
E, Weinan; Han, Jiequn; Li, Qianxiao
8
2019
Optimal partition and effective dynamics of complex networks. Zbl 1205.68031
E, Weinan; Li, Tiejun; Vanden-Eijnden, Eric
8
2008
The heterogeneous multiscale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems. Zbl 1080.65090
Chen, Shanqin; E, Weinan; Shu, Chi-Wang
8
2005
Turbulent Prandtl number effect on passive scalar advection. Zbl 0986.76025
E, Weinan; Vanden-Eijnden, Eric
8
2001
Recent results on mathematical and statistical hydrodynamics. Zbl 0983.76010
E, Weinan; Sinai, Yakov
8
2000
PDFs for velocity and velocity gradients in Burgers’ turbulence. Zbl 1027.76592
Avellaneda, M.; Ryan, R.; E, Weinan
8
1995
On the distinguished limits of the Navier slip model of the moving contact line problem. Zbl 1327.76019
Ren, Weiqing; Trinh, Philippe H.; E., Weinan
7
2015
Model the nonlinear instability of wall-bounded shear flows as a rare event: a study on two-dimensional Poiseuille flow. Zbl 1316.35246
Wan, Xiaoliang; Yu, Haijun; Weinan, E.
7
2015
A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics. Zbl 1453.68163
E, Weinan; Ma, Chao; Wu, Lei
2
2020
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. Zbl 1442.91116
Beck, Christian; E, Weinan; Jentzen, Arnulf
19
2019
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations. Zbl 1418.65149
E, Weinan; Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
14
2019
A mean-field optimal control formulation of deep learning. Zbl 1421.49021
E, Weinan; Han, Jiequn; Li, Qianxiao
8
2019
A priori estimates of the population risk for two-layer neural networks. Zbl 1427.68277
Weinan, E.; Ma, Chao; Wu, Lei
3
2019
Stochastic modified equations and dynamics of stochastic gradient algorithms. I: Mathematical foundations. Zbl 07049759
Li, Qianxiao; Tai, Cheng; E, Weinan
2
2019
Machine learning: mathematical theory and scientific applications. Zbl 1439.68019
E, Weinan
1
2019
Solving high-dimensional partial differential equations using deep learning. Zbl 1416.35137
Han, Jiequn; Jentzen, Arnulf; E, Weinan
42
2018
The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems. Zbl 1392.35306
E, Weinan; Yu, Bing
33
2018
Maximum principle based algorithms for deep learning. Zbl 06982921
Li, Qianxiao; Chen, Long; Tai, Cheng; E, Weinan
4
2018
Exponential convergence of the deep neural network approximation for analytic functions. Zbl 06967359
E., Weinan; Wang, Qingcan
4
2018
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Zbl 1382.65016
E, Weinan; Han, Jiequn; Jentzen, Arnulf
58
2017
A proposal on machine learning via dynamical systems. Zbl 1380.37154
E, Weinan
19
2017
Noisy Hegselmann-Krause systems: phase transition and the \(2R\)-conjecture. Zbl 1393.82013
Wang, Chu; Li, Qianxiao; E, Weinan; Chazelle, Bernard
3
2017
Optimal convergence rate of the universal estimation error. Zbl 1361.62024
Weinan, E.; Wang, Yao
1
2017
Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations. Zbl 1342.60094
E, Weinan; Jentzen, Arnulf; Shen, Hao
5
2016
On the distinguished limits of the Navier slip model of the moving contact line problem. Zbl 1327.76019
Ren, Weiqing; Trinh, Philippe H.; E., Weinan
7
2015
Model the nonlinear instability of wall-bounded shear flows as a rare event: a study on two-dimensional Poiseuille flow. Zbl 1316.35246
Wan, Xiaoliang; Yu, Haijun; Weinan, E.
7
2015
The free action of nonequilibrium dynamics. Zbl 1327.82060
Li, Qianxiao; E, Weinan
1
2015
The Kohn-Sham equation for deformed crystals. Zbl 1435.74001
E, Weinan; Lu, Jianfeng
12
2013
Optimization-based string method for finding minimum energy path. Zbl 1373.37062
Samanta, Amit; E, Weinan
4
2013
Asymptotic analysis of quantum dynamics in crystals: the Bloch-Wigner transform, Bloch dynamics and Berry phase. Zbl 1278.81084
E, Weinan; Lu, Jian-feng; Yang, Xu
4
2013
Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory. Zbl 1349.65168
Lin, Lin; Shao, Sihong; E, Weinan
1
2013
Mean field limit of a dynamical model of polymer systems. Zbl 1301.60071
E, Weinan; Shen, Hao
1
2013
The heterogeneous multiscale method. Zbl 1255.65224
Abdulle, Assyr; Weinan, E.; Engquist, Björn; Vanden-Eijnden, Eric
113
2012
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework. I: Total energy calculation. Zbl 1251.82008
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
23
2012
Optimized local basis set for Kohn-Sham density functional theory. Zbl 1250.82002
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
6
2012
Subcritical bifurcation in spatially extended systems. Zbl 1275.60054
E, Weinan; Zhou, Xiang; Cheng, Xiuyuan
3
2012
Stability and the continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model. Zbl 1278.82054
E, Weinan; Lu, Jianfeng
1
2012
Principles of multiscale modeling. Zbl 1238.00010
E, Weinan
57
2011
The gentlest ascent dynamics. Zbl 1237.37052
E, Weinan; Zhou, Xiang
18
2011
SelInv – an algorithm for selected inversion of a sparse symmetric matrix. Zbl 1365.65069
Lin, Lin; Yang, Chao; Meza, Juan C.; Lu, Jianfeng; Ying, Lexing; E, Weinan
17
2011
The electronic structure of smoothly deformed crystals: Wannier functions and the Cauchy-Born Rule. Zbl 1253.74025
E, Weinan; Lu, Jianfeng
15
2011
A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations. Zbl 1230.65039
Lin, Lin; Yang, Chao; Lu, Jianfeng; Ying, Lexing; E, Weinan
10
2011
Derivation of continuum models for the moving contact line problem based on thermodynamic principles. Zbl 1414.76019
Ren, Weiqing; E, Weinan
10
2011
Contact line dynamics on heterogeneous surfaces. Zbl 1308.76212
Ren, Weiqing; E, Weinan
7
2011
Effective Maxwell equations from time-dependent density functional theory. Zbl 1210.81030
Weinan, E.; Lu, Jianfeng; Yang, Xu
4
2011
The heterogeneous multiscale methods with application to combustion. Zbl 1380.76098
E., Weinan; Engquist, Björn; Sun, Yi
2
2011
Continuum models for the contact line problem. Zbl 1308.76082
Ren, Weiqing; Hu, Dan; Weinan, E.
19
2010
Study of the noise-induced transition and the exploration of the phase space for the Kuramoto-Sivashinsky equation using the minimum action method. Zbl 1185.82044
Wan, X.; Zhou, X.; E, W.
15
2010
Study of noise-induced transitions in the Lorenz system using the minimum action method. Zbl 1202.34104
Zhou, Xiang; E, Weinan
13
2010
Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model. Zbl 1277.81117
E, Weinan; Lu, Jianfeng
12
2010
Localized bases of eigensubspaces and operator compression. Zbl 1205.15017
E, Weinan; Li, Tiejun; Lu, Jianfeng
11
2010
A multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks. Zbl 1423.74958
Li, Xiantao; Yang, Jerry Z.; E, Weinan
7
2010
A numerical method for the study of nucleation of ordered phases. Zbl 1329.82041
Lin, Ling; Cheng, Xiuyuan; E, Weinan; Shi, An-Chang; Zhang, Pingwen
7
2010
On the crystallization of 2D hexagonal lattices. Zbl 1180.82191
E, Weinan; Li, Dong
32
2009
Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems. Zbl 1182.65072
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Car, Roberto; E, Weinan
25
2009
A general strategy for designing seamless multiscale methods. Zbl 1280.76038
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
12
2009
Pole-based approximation of the Fermi-Dirac function. Zbl 1188.41007
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Weinan, E.
9
2009
Orbital minimization with localization. Zbl 1170.46313
Gao, Weiguo; E, Weinan
2
2009
Effectiveness of implicit methods for stiff stochastic differential equations. Zbl 1199.65010
Li, Tiejun; Abdulle, Assyr; Weinan, E
15
2008
Optimal partition and effective dynamics of complex networks. Zbl 1205.68031
E, Weinan; Li, Tiejun; Vanden-Eijnden, Eric
8
2008
The Andersen thermostat in molecular dynamics. Zbl 1148.82019
E, Weinan; Li, Dong
6
2008
Breakdown of homogenization for the random Hamilton-Jacobi equations. Zbl 1207.70018
E, Weinan; Wehr, Jan; Xin, Jack
1
2008
Heterogeneous multiscale methods: a review. Zbl 1164.65496
E, Weinan; Engquist, Bjorn; Li, Xiantao; Ren, Weiqing; Vanden-Eijnden, Eric
138
2007
Cauchy-Born rule and the stability of crystalline solids: Static problems. Zbl 1106.74019
E, Weinan; Ming, Pingbing
58
2007
Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales. Zbl 1162.80003
E, Weinan; Liu, Di; Vanden-Eijnden, Eric
31
2007
The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size. Zbl 1158.74541
Yue, Xingye; E, Weinan
28
2007
Boundary conditions for the moving contact line problem. Zbl 1146.76513
Ren, Weiqing; E, Weinan
26
2007
Cauchy-Born rule and the stability of crystalline solids: dynamic problems. Zbl 1138.35063
E, Weinan; Ming, Pingbing
17
2007
A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations. Zbl 1343.76041
Chen, Shanqin; E, Weinan; Liu, Yunxian; Shu, Chi-Wang
7
2007
The elastic continuum limit of the tight binding model. Zbl 1136.74003
E, Weinan; Lu, Jianfeng
6
2007
A sub-linear scaling algorithm for computing the electronic structure of materials. Zbl 1133.35429
García-Cervera, Carlos J.; Lu, Jianfeng; E, Weinan
3
2007
Seamless multiscale modeling via dynamics on fiber bundles. Zbl 1133.65029
E, Weinan; Lu, Jianfeng
2
2007
Towards a theory of transition paths. Zbl 1101.82016
E, Weinan; Vanden-Eijnden, Eric
31
2006
Variational boundary conditions for molecular dynamics simulations of solids at low temperature. Zbl 1114.74326
Li, Xiantao; E, Weinan
19
2006
A molecular kinetic theory of inhomogeneous liquid crystal flow and the small Deborah number limit. Zbl 1131.76010
E, Weinan; Zhang, Pingwen
13
2006
Simulations of 3-D domain wall structures in thin films. Zbl 1099.35153
Wang, Xiao-Ping; Wang, Ke; E, Weinan
2
2006
Analysis of the heterogeneous multiscale method for elliptic homogenization problems. Zbl 1060.65118
E, Weinan; Ming, Pingbing; Zhang, Pingwen
90
2005
Analysis of multiscale methods for stochastic differential equations. Zbl 1080.60060
E, Weinan; Liu, Di; Vanden-Eijnden, Eric
43
2005
Multiscale modeling of the dynamics of solids at finite temperature. Zbl 1120.74313
Li, Xiantao; E, Weinan
33
2005
Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics. Zbl 1143.76541
Ren, Weiqing; E, Weinan
30
2005
The heterogeneous multi-scale method for homogenization problems. Zbl 1086.65521
E, Weinan; Engquist, Björn
19
2005
Self-induced stochastic resonance in excitable systems. Zbl 1109.34040
Muratov, Cyrill B.; Vanden-Eijnden, Eric; E, Weinan
13
2005
Analysis of the local quasicontinuum method. Zbl 1188.74019
E, Weinan; Ming, Pingbing
10
2005
Numerical methods for multiscale transport equations and application to two-phase porous media flow. Zbl 1089.76049
Yue, Xingye; E, Weinan
9
2005
The heterogeneous multiscale method based on the discontinuous Galerkin method for hyperbolic and parabolic problems. Zbl 1080.65090
Chen, Shanqin; E, Weinan; Shu, Chi-Wang
8
2005
Minimum action method for the study of rare events. Zbl 1050.60068
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
81
2004
A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow. Zbl 1059.76060
Nie, X. B.; Chen, S. Y.; E, Weinan; Robbins, M. O.
40
2004
Well-posedness for the dumbbell model of polymeric fluids. Zbl 1060.35169
E, Weinan; Li, Tiejun; Zhang, Pingwen
38
2004
Some recent progress in multiscale modeling. Zbl 1419.74252
E, Weinan; Li, Xiantao; Vanden-Eijnden, Eric
19
2004
Analysis of multiscale methods. Zbl 1046.65108
E, Weinan; Ming, Pingbing
11
2004
Metastability, conformation dynamics, and transition pathways in complex systems. Zbl 1141.82312
E, Weinan; Vanden-Eijnden, Eric
10
2004
Stochastic models of polymeric fluids at small Deborah number. Zbl 1078.76009
Li, T.; Vanden-Eijnden, E.; Zhang, P.; E, W.
6
2004
Analysis of the heterogeneous multiscale method for gas dynamics. Zbl 1177.76355
E, Weinan; Li, Xiantao
3
2004
The heterogeneous multi-scale method. Zbl 1328.74087
E, Weinan; Engquist, Bjorn
1
2004
Heterogeneous multiscale method for locally self-similar problems. Zbl 1081.82563
E, Weinan; Yue, Xing Y.
1
2004
The heterogeneous multiscale methods. Zbl 1093.35012
E, Weinan; Engquist, Bjorn
320
2003
Gauge method for viscous incompressible flows. Zbl 1160.76329
E, Weinan; Liu, Jian-Guo
44
2003
Multiscale modeling and computation. Zbl 1032.65013
E, Weinan; Engquist, Bjorn
39
2003
Finite difference heterogeneous multi-scale method for homogenization problems. Zbl 1034.65067
Abdulle, Assyr; E, Weinan
35
2003
Analysis of the heterogeneous multiscale method for ordinary differential equations. Zbl 1088.65552
E, Weinan
29
2003
Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth. Zbl 1023.82007
Schulze, Tim P.; Smereka, Peter; E, Weinan
9
2003
A note on generalized flows. Zbl 1042.34009
E, Weinan; Vanden-Eijnden, Eric
6
2003
Accurate numerical methods for micromagnetics simulations with general geometries. Zbl 1036.78016
García-Cervera, Carlos J.; Gimbutas, Zydrunas; E, Weinan
6
2003
A dynamic atomistic–continuum method for the simulation of crystalline materials. Zbl 1013.82022
E, Weinan; Huang, Zhongyi
36
2002
Energy landscapes and rare events. Zbl 1023.65004
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
12
2002
Projection method. III: Spatial discretization on the staggered grid. Zbl 1058.76043
E, Weinan; Liu, Jian-Guo
12
2002
Gibbsian dynamics and invariant measures for stochastic dissipative PDEs. Zbl 1023.60057
E, Weinan; Liu, Di
9
2002
Convergence of a stochastic method for the modeling of polymeric fluids. Zbl 1137.76313
E, Weinan; Li, Tiejun; Zhang, Pingwen
6
2002
...and 54 more Documents
all top 5

Cited by 3,468 Authors

56 E, Weinan
41 Abdulle, Assyr
35 Lu, Jianfeng
29 Vanden-Eijnden, Eric
27 Chung, Tsz Shun Eric
26 Liu, Jianguo
21 Efendiev, Yalchin R.
19 Ortner, Christoph
17 Cui, Junzhi
16 Lin, Lin
16 Ying, Lexing
16 Zhang, Pingwen
15 Constantin, Peter
15 Du, Qiang
15 Masmoudi, Nader
15 Wang, Cheng
14 Hou, Thomas Yizhao
14 Yang, Hanchun
13 Eyink, Gregory L.
13 Majda, Andrew J.
13 Ren, Weiqing
13 Shen, Jie
13 Vicol, Vlad C.
13 Wang, Xiaoming
12 Samaey, Giovanni
12 Wu, Jiahong
12 Zhang, Zhifei
11 Leung, Wingtat
11 Li, Xiantao
11 Liu, Wing Kam
11 Ohlberger, Mario
11 Schütte, Christof
11 Yang, Tong
11 Yang, Xiaofeng
10 Bakhtin, Yuri Yu.
10 Engquist, Bjorn E.
10 Henning, Patrick
10 Liu, Cheng-Jie
10 Luskin, Mitchell
10 Mattingly, Jonathan C.
10 Ming, Pingbing
10 Titi, Edriss Saleh
10 Vilmart, Gilles
9 De Lellis, Camillo
9 Stefanelli, Ulisse
9 Székelyhidi, László jun.
9 Tang, Shaoqiang
9 Vasilyeva, Maria V.
9 Yue, Xingye
8 Cameron, Maria Kourkina
8 Drivas, Theodore Dimitrios
8 Fish, Jacob
8 Gloria, Antoine
8 Hairer, Martin
8 Jentzen, Arnulf
8 Karniadakis, George Em
8 Kuksin, Sergeĭ B.
8 Le Bris, Claude
8 Lelièvre, Tony
8 Mishra, Siddhartha
8 Süli, Endre E.
8 Valentin, Frédéric
8 Wang, Shu
8 Wang, Ya-Guang
8 Yang, Zhiqiang
8 Zabaras, Nicholas J.
8 Zhao, Huaizhong
7 Bao, Weizhu
7 Bétermin, Laurent
7 Chen, Gui-Qiang G.
7 Debussche, Arnaud
7 Degond, Pierre
7 Friedrich, Manuel
7 García-Cervera, Carlos J.
7 Glatt-Holtz, Nathan E.
7 Gosse, Laurent
7 Guo, Boling
7 Hartmann, Carsten
7 Hoang, Viet Ha
7 Isett, Philip
7 Jung, Changyeol
7 Kevrekidis, Ioannis George
7 Kukavica, Igor
7 Legoll, Frédéric
7 Lin, Fang Hua
7 Liu, Di
7 Lötstedt, Per
7 Nedeljkov, Marko
7 Osher, Stanley Joel
7 Owhadi, Houman
7 Pavliotis, Grigorios A.
7 Peterseim, Daniel
7 Shelkovich, Vladimir M.
7 Shirikyan, Armen R.
7 Tadmor, Eitan
7 Tao, Wenquan
7 Temam, Roger Meyer
7 Wang, Wei
7 Wang, Wei
7 Yao, Zhengan
...and 3,368 more Authors
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Cited in 297 Serials

288 Journal of Computational Physics
99 Computer Methods in Applied Mechanics and Engineering
89 Archive for Rational Mechanics and Analysis
83 Multiscale Modeling & Simulation
66 Journal of Differential Equations
62 Journal of Computational and Applied Mathematics
62 Physica D
55 Communications in Mathematical Physics
55 Journal of Scientific Computing
51 Journal of Statistical Physics
36 Journal of Mathematical Analysis and Applications
36 Mathematics of Computation
36 SIAM Journal on Mathematical Analysis
34 Computers and Fluids
33 Journal of Mathematical Physics
31 Journal of Fluid Mechanics
31 Journal of Nonlinear Science
31 SIAM Journal on Scientific Computing
31 Physics of Fluids
30 Communications on Pure and Applied Mathematics
30 Computational Mechanics
28 Applied Numerical Mathematics
27 Computers & Mathematics with Applications
27 International Journal for Numerical Methods in Engineering
24 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
23 Nonlinearity
23 SIAM Journal on Numerical Analysis
23 Stochastic Processes and their Applications
23 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
19 Applied Mathematics and Computation
19 Journal of Functional Analysis
19 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
18 Discrete and Continuous Dynamical Systems
18 Science China. Mathematics
17 Numerische Mathematik
17 Chaos
16 Discrete and Continuous Dynamical Systems. Series B
14 Applicable Analysis
14 International Journal for Numerical Methods in Fluids
14 Communications in Partial Differential Equations
14 Advances in Computational Mathematics
14 Journal of Mathematical Fluid Mechanics
14 Comptes Rendus. Mathématique. Académie des Sciences, Paris
13 Applied Mathematics Letters
12 Journal of the Mechanics and Physics of Solids
12 Proceedings of the American Mathematical Society
12 Probability Theory and Related Fields
12 Discrete and Continuous Dynamical Systems. Series S
12 Research in the Mathematical Sciences
11 ZAMP. Zeitschrift für angewandte Mathematik und Physik
11 The Annals of Probability
11 BIT
11 Transactions of the American Mathematical Society
11 Journal de Mathématiques Pures et Appliquées. Neuvième Série
11 SIAM Journal on Applied Mathematics
11 Calculus of Variations and Partial Differential Equations
11 Mathematical Problems in Engineering
11 Computational Geosciences
10 Advances in Mathematics
10 Chinese Annals of Mathematics. Series B
9 The Annals of Applied Probability
9 Nonlinear Analysis. Real World Applications
9 Stochastic and Partial Differential Equations. Analysis and Computations
8 Bulletin of Mathematical Biology
8 Quarterly of Applied Mathematics
8 Advances in Mathematical Physics
8 Annals of PDE
7 Mathematical Methods in the Applied Sciences
7 Acta Mathematicae Applicatae Sinica. English Series
7 Numerical Methods for Partial Differential Equations
7 Proceedings of the National Academy of Sciences of the United States of America
7 Bulletin of the American Mathematical Society. New Series
7 Journal of Mathematical Imaging and Vision
7 Journal of Mathematical Sciences (New York)
7 Abstract and Applied Analysis
7 Communications on Pure and Applied Analysis
7 SIAM Journal on Applied Dynamical Systems
7 Acta Numerica
6 Mathematics and Computers in Simulation
6 Acta Applicandae Mathematicae
6 Journal of the American Mathematical Society
6 Science in China. Series A
6 European Journal of Applied Mathematics
6 Applied Mathematical Modelling
6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
6 SIAM Review
6 Continuum Mechanics and Thermodynamics
6 Journal of Hyperbolic Differential Equations
6 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
5 Duke Mathematical Journal
5 International Journal of Computer Mathematics
5 Journal of Mathematical Chemistry
5 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
5 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
5 Acta Mathematica Sinica. English Series
5 Archives of Computational Methods in Engineering
5 Foundations of Computational Mathematics
5 Acta Mechanica Sinica
5 Journal of Physics A: Mathematical and Theoretical
...and 197 more Serials
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Cited in 45 Fields

1,234 Partial differential equations (35-XX)
1,009 Fluid mechanics (76-XX)
889 Numerical analysis (65-XX)
422 Probability theory and stochastic processes (60-XX)
354 Statistical mechanics, structure of matter (82-XX)
324 Mechanics of deformable solids (74-XX)
149 Dynamical systems and ergodic theory (37-XX)
102 Ordinary differential equations (34-XX)
95 Calculus of variations and optimal control; optimization (49-XX)
92 Biology and other natural sciences (92-XX)
75 Computer science (68-XX)
65 Optics, electromagnetic theory (78-XX)
55 Quantum theory (81-XX)
47 Classical thermodynamics, heat transfer (80-XX)
44 Mechanics of particles and systems (70-XX)
39 Statistics (62-XX)
38 Geophysics (86-XX)
38 Systems theory; control (93-XX)
24 Operations research, mathematical programming (90-XX)
23 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
22 Global analysis, analysis on manifolds (58-XX)
20 Functional analysis (46-XX)
16 Approximations and expansions (41-XX)
16 Information and communication theory, circuits (94-XX)
15 Real functions (26-XX)
13 Linear and multilinear algebra; matrix theory (15-XX)
13 Harmonic analysis on Euclidean spaces (42-XX)
13 Operator theory (47-XX)
11 Integral equations (45-XX)
11 Differential geometry (53-XX)
7 Measure and integration (28-XX)
7 Astronomy and astrophysics (85-XX)
6 General and overarching topics; collections (00-XX)
6 Combinatorics (05-XX)
5 Difference and functional equations (39-XX)
5 Convex and discrete geometry (52-XX)
4 History and biography (01-XX)
4 Potential theory (31-XX)
4 Relativity and gravitational theory (83-XX)
2 Algebraic geometry (14-XX)
2 Functions of a complex variable (30-XX)
2 Special functions (33-XX)
1 Number theory (11-XX)
1 Several complex variables and analytic spaces (32-XX)
1 General topology (54-XX)

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