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## E, Weinan

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 Author ID: 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
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#### 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
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#### 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
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#### Fields

 65 Fluid mechanics (76-XX) 61 Partial differential equations (35-XX) 59 Numerical analysis (65-XX) 42 Statistical mechanics, structure of matter (82-XX) 27 Mechanics of deformable solids (74-XX) 26 Probability theory and stochastic processes (60-XX) 17 Computer science (68-XX) 12 Dynamical systems and ergodic theory (37-XX) 12 Quantum theory (81-XX) 9 Ordinary differential equations (34-XX) 6 Statistics (62-XX) 5 General and overarching topics; collections (00-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Approximations and expansions (41-XX) 4 Functional analysis (46-XX) 4 Optics, electromagnetic theory (78-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Biology and other natural sciences (92-XX) 3 Mechanics of particles and systems (70-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Algebraic topology (55-XX) 1 Information and communication theory, circuits (94-XX)

#### 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
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.
1996
Onsager’s conjecture on the energy conservation for solutions of Euler’s equation. Zbl 0818.35085
Constantin, Peter; E, Weinan; Titi, Edriss S.
1994
Heterogeneous multiscale methods: a review. Zbl 1164.65496
E, Weinan; Engquist, Bjorn; Li, Xiantao; Ren, Weiqing; Vanden-Eijnden, Eric
2007
The heterogeneous multiscale method. Zbl 1255.65224
Abdulle, Assyr; Weinan, E.; Engquist, Björn; Vanden-Eijnden, Eric
2012
Invariant measures for Burgers equation with stochastic forcing. Zbl 0972.35196
E, Weinan; Khanin, K.; Mazel, A.; Sinai, Ya.
2000
Analysis of the heterogeneous multiscale method for elliptic homogenization problems. Zbl 1060.65118
E, Weinan; Ming, Pingbing; Zhang, Pingwen
2005
Blowup of solutions of the unsteady Prandtl’s equation. Zbl 0908.35099
E, Weinan; Engquist, Bjorn
1997
Minimum action method for the study of rare events. Zbl 1050.60068
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
2004
Projection method. I: Convergence and numerical boundary layers. Zbl 0842.76052
E, Weinan; Liu, Jian-Guo
1995
Boundary layer theory and the zero-viscosity limit of the Navier-Stokes equation. Zbl 0961.35101
E, Weinan
2000
Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation. Zbl 0994.60065
E, Weinan; Mattingly, J. C.; Sinai, Ya.
2001
Vorticity boundary condition and related isssues for finite difference schemes. Zbl 0847.76050
E, Weinan; Liu, Jian-Guo
1996
Small-scale structures in Boussinesq convection. Zbl 0822.76087
E, Weinan; Shu, Chi-Wang
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
2017
Cauchy-Born rule and the stability of crystalline solids: Static problems. Zbl 1106.74019
E, Weinan; Ming, Pingbing
2007
Principles of multiscale modeling. Zbl 1238.00010
E, Weinan
2011
Essentially compact schemes for unsteady viscous incompressible flows. Zbl 0853.76045
E, Weinan; Liu, Jian-Guo
1996
Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity. Zbl 0814.34039
E, Weinan
1994
Homogenization of linear and nonlinear transport equations. Zbl 0794.35014
E, Weinan
1992
Gauge method for viscous incompressible flows. Zbl 1160.76329
E, Weinan; Liu, Jian-Guo
2003
Analysis of multiscale methods for stochastic differential equations. Zbl 1080.60060
E, Weinan; Liu, Di; Vanden-Eijnden, Eric
2005
Solving high-dimensional partial differential equations using deep learning. Zbl 1416.35137
Han, Jiequn; Jentzen, Arnulf; E, Weinan
2018
Numerical methods for the Landau–Lifshitz equation. Zbl 0988.65079
E, Weinan; Wang, Xiao-Ping
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.
2004
Multiscale modeling and computation. Zbl 1032.65013
E, Weinan; Engquist, Bjorn
2003
Ergodicity for the Navier-Stokes equation with degenerate random forcing: finite-dimensional approximation. Zbl 1024.76012
E, Weinan; Mattingly, Jonathan C.
2001
Well-posedness for the dumbbell model of polymeric fluids. Zbl 1060.35169
E, Weinan; Li, Tiejun; Zhang, Pingwen
2004
A dynamic atomistic–continuum method for the simulation of crystalline materials. Zbl 1013.82022
E, Weinan; Huang, Zhongyi
2002
Finite difference heterogeneous multi-scale method for homogenization problems. Zbl 1034.65067
Abdulle, Assyr; E, Weinan
2003
The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems. Zbl 1392.35306
E, Weinan; Yu, Bing
2018
Multiscale modeling of the dynamics of solids at finite temperature. Zbl 1120.74313
Li, Xiantao; E, Weinan
2005
On the crystallization of 2D hexagonal lattices. Zbl 1180.82191
E, Weinan; Li, Dong
2009
Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales. Zbl 1162.80003
E, Weinan; Liu, Di; Vanden-Eijnden, Eric
2007
Towards a theory of transition paths. Zbl 1101.82016
E, Weinan; Vanden-Eijnden, Eric
2006
Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics. Zbl 1143.76541
Ren, Weiqing; E, Weinan
2005
Analysis of the heterogeneous multiscale method for ordinary differential equations. Zbl 1088.65552
E, Weinan
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
2007
Boundary conditions for the moving contact line problem. Zbl 1146.76513
Ren, Weiqing; E, Weinan
2007
A Gauss-Seidel projection method for micromagnetics simulations. Zbl 1012.82002
Wang, Xiao-Ping; García-Cervera, Carlos J.; E, Weinan
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
2009
Statistical properties of shocks in Burgers turbulence. Zbl 0844.35144
Avellaneda, Marco; E, Weinan
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
2012
A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow. Zbl 0790.76055
E, Weinan; Shu, Chi-Wang
1994
Aubry-Mather theory and periodic solutions of the forced Burgers equation. Zbl 0916.35099
E, Weinan
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
1997
Projection method. II: Godunov-Ryabenki analysis. Zbl 0920.76056
E, Weinan; Liu, Jian-Guo
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
2019
A proposal on machine learning via dynamical systems. Zbl 1380.37154
E, Weinan
2017
Continuum models for the contact line problem. Zbl 1308.76082
Ren, Weiqing; Hu, Dan; Weinan, E.
2010
Variational boundary conditions for molecular dynamics simulations of solids at low temperature. Zbl 1114.74326
Li, Xiantao; E, Weinan
2006
The heterogeneous multi-scale method for homogenization problems. Zbl 1086.65521
E, Weinan; Engquist, Björn
2005
Some recent progress in multiscale modeling. Zbl 1419.74252
E, Weinan; Li, Xiantao; Vanden-Eijnden, Eric
2004
The gentlest ascent dynamics. Zbl 1237.37052
E, Weinan; Zhou, Xiang
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
2011
Cauchy-Born rule and the stability of crystalline solids: dynamic problems. Zbl 1138.35063
E, Weinan; Ming, Pingbing
2007
Generalized flows, intrinsic stochasticity, and turbulent transport. Zbl 0967.76038
E, Weinan; Vanden Eijnden, Eric
2000
Nonlinear continuum theory of smectic-$$A$$ liquid crystals. Zbl 0891.76009
E, Weinan
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.
1991
The electronic structure of smoothly deformed crystals: Wannier functions and the Cauchy-Born Rule. Zbl 1253.74025
E, Weinan; Lu, Jianfeng
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.
2010
Effectiveness of implicit methods for stiff stochastic differential equations. Zbl 1199.65010
Li, Tiejun; Abdulle, Assyr; Weinan, E
2008
Statistical theory for the stochastic Burgers equation in the inviscid limit. Zbl 1037.76013
E, Weinan; Vanden Eijnden, Eric
2000
Finite difference schemes for incompressible flows in the velocity-impulse density formulation. Zbl 0870.76048
E, Weinan; Liu, Jian-Guo
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
2019
Continuum theory of epitaxial crystal growth. I. Zbl 1074.76504
E, Weinan; Yip, Nung Kwan
2001
Study of noise-induced transitions in the Lorenz system using the minimum action method. Zbl 1202.34104
Zhou, Xiang; E, Weinan
2010
A molecular kinetic theory of inhomogeneous liquid crystal flow and the small Deborah number limit. Zbl 1131.76010
E, Weinan; Zhang, Pingwen
2006
Self-induced stochastic resonance in excitable systems. Zbl 1109.34040
Muratov, Cyrill B.; Vanden-Eijnden, Eric; E, Weinan
2005
Large time behavior and homogenization of solutions of two-dimensional conservation laws. Zbl 0797.35114
Engquist, Bjorn; E, Weinan
1993
Homogenization of scalar conservation laws with oscillatory forcing terms. Zbl 0755.35068
E, Weinan
1992
The Kohn-Sham equation for deformed crystals. Zbl 1435.74001
E, Weinan; Lu, Jianfeng
2013
Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model. Zbl 1277.81117
E, Weinan; Lu, Jianfeng
2010
A general strategy for designing seamless multiscale methods. Zbl 1280.76038
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
2009
Energy landscapes and rare events. Zbl 1023.65004
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
2002
Projection method. III: Spatial discretization on the staggered grid. Zbl 1058.76043
E, Weinan; Liu, Jian-Guo
2002
Convergence of Fourier methods for the Navier-Stokes equations. Zbl 0776.76021
E, Weinan
1993
A class of homogenization problems in the calculus of variations. Zbl 0773.49007
E, Weinan
1991
Localized bases of eigensubspaces and operator compression. Zbl 1205.15017
E, Weinan; Li, Tiejun; Lu, Jianfeng
2010
Analysis of multiscale methods. Zbl 1046.65108
E, Weinan; Ming, Pingbing
2004
Convergence of spectral methods for Burgers’ equation. Zbl 0764.65057
E, Weinan
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
2011
Derivation of continuum models for the moving contact line problem based on thermodynamic principles. Zbl 1414.76019
Ren, Weiqing; E, Weinan
2011
Analysis of the local quasicontinuum method. Zbl 1188.74019
E, Weinan; Ming, Pingbing
2005
Metastability, conformation dynamics, and transition pathways in complex systems. Zbl 1141.82312
E, Weinan; Vanden-Eijnden, Eric
2004
Simple finite element method in vorticity formulation for incompressible flows. Zbl 0977.76048
Liu, Jian-Guo; E, Weinan
2001
Phase separation in incompressible systems. Zbl 1110.82304
E, Weinan; Palffy-Muhoray, P.
1997
Correctors for the homogenization of conservation laws with oscillatory forcing terms. Zbl 0766.35026
Weinan, E.; Serre, Denis
1992
Pole-based approximation of the Fermi-Dirac function. Zbl 1188.41007
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Weinan, E.
2009
Numerical methods for multiscale transport equations and application to two-phase porous media flow. Zbl 1089.76049
Yue, Xingye; E, Weinan
2005
Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth. Zbl 1023.82007
Schulze, Tim P.; Smereka, Peter; E, Weinan
2003
Gibbsian dynamics and invariant measures for stochastic dissipative PDEs. Zbl 1023.60057
E, Weinan; Liu, Di
2002
A mean-field optimal control formulation of deep learning. Zbl 1421.49021
E, Weinan; Han, Jiequn; Li, Qianxiao
2019
Optimal partition and effective dynamics of complex networks. Zbl 1205.68031
E, Weinan; Li, Tiejun; Vanden-Eijnden, Eric
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
2005
Turbulent Prandtl number effect on passive scalar advection. Zbl 0986.76025
E, Weinan; Vanden-Eijnden, Eric
2001
Recent results on mathematical and statistical hydrodynamics. Zbl 0983.76010
E, Weinan; Sinai, Yakov
2000
PDFs for velocity and velocity gradients in Burgers’ turbulence. Zbl 1027.76592
Avellaneda, M.; Ryan, R.; E, Weinan
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
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.
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
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
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
2019
A mean-field optimal control formulation of deep learning. Zbl 1421.49021
E, Weinan; Han, Jiequn; Li, Qianxiao
2019
A priori estimates of the population risk for two-layer neural networks. Zbl 1427.68277
Weinan, E.; Ma, Chao; Wu, Lei
2019
Stochastic modified equations and dynamics of stochastic gradient algorithms. I: Mathematical foundations. Zbl 07049759
Li, Qianxiao; Tai, Cheng; E, Weinan
2019
Machine learning: mathematical theory and scientific applications. Zbl 1439.68019
E, Weinan
2019
Solving high-dimensional partial differential equations using deep learning. Zbl 1416.35137
Han, Jiequn; Jentzen, Arnulf; E, Weinan
2018
The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems. Zbl 1392.35306
E, Weinan; Yu, Bing
2018
Maximum principle based algorithms for deep learning. Zbl 06982921
Li, Qianxiao; Chen, Long; Tai, Cheng; E, Weinan
2018
Exponential convergence of the deep neural network approximation for analytic functions. Zbl 06967359
E., Weinan; Wang, Qingcan
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
2017
A proposal on machine learning via dynamical systems. Zbl 1380.37154
E, Weinan
2017
Noisy Hegselmann-Krause systems: phase transition and the $$2R$$-conjecture. Zbl 1393.82013
Wang, Chu; Li, Qianxiao; E, Weinan; Chazelle, Bernard
2017
Optimal convergence rate of the universal estimation error. Zbl 1361.62024
Weinan, E.; Wang, Yao
2017
Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations. Zbl 1342.60094
E, Weinan; Jentzen, Arnulf; Shen, Hao
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
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.
2015
The free action of nonequilibrium dynamics. Zbl 1327.82060
Li, Qianxiao; E, Weinan
2015
The Kohn-Sham equation for deformed crystals. Zbl 1435.74001
E, Weinan; Lu, Jianfeng
2013
Optimization-based string method for finding minimum energy path. Zbl 1373.37062
Samanta, Amit; E, Weinan
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
2013
Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory. Zbl 1349.65168
Lin, Lin; Shao, Sihong; E, Weinan
2013
Mean field limit of a dynamical model of polymer systems. Zbl 1301.60071
E, Weinan; Shen, Hao
2013
The heterogeneous multiscale method. Zbl 1255.65224
Abdulle, Assyr; Weinan, E.; Engquist, Björn; Vanden-Eijnden, Eric
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
2012
Optimized local basis set for Kohn-Sham density functional theory. Zbl 1250.82002
Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
2012
Subcritical bifurcation in spatially extended systems. Zbl 1275.60054
E, Weinan; Zhou, Xiang; Cheng, Xiuyuan
2012
Stability and the continuum limit of the spin-polarized Thomas-Fermi-Dirac-von Weizsäcker model. Zbl 1278.82054
E, Weinan; Lu, Jianfeng
2012
Principles of multiscale modeling. Zbl 1238.00010
E, Weinan
2011
The gentlest ascent dynamics. Zbl 1237.37052
E, Weinan; Zhou, Xiang
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
2011
The electronic structure of smoothly deformed crystals: Wannier functions and the Cauchy-Born Rule. Zbl 1253.74025
E, Weinan; Lu, Jianfeng
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
2011
Derivation of continuum models for the moving contact line problem based on thermodynamic principles. Zbl 1414.76019
Ren, Weiqing; E, Weinan
2011
Contact line dynamics on heterogeneous surfaces. Zbl 1308.76212
Ren, Weiqing; E, Weinan
2011
Effective Maxwell equations from time-dependent density functional theory. Zbl 1210.81030
Weinan, E.; Lu, Jianfeng; Yang, Xu
2011
The heterogeneous multiscale methods with application to combustion. Zbl 1380.76098
E., Weinan; Engquist, Björn; Sun, Yi
2011
Continuum models for the contact line problem. Zbl 1308.76082
Ren, Weiqing; Hu, Dan; Weinan, E.
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.
2010
Study of noise-induced transitions in the Lorenz system using the minimum action method. Zbl 1202.34104
Zhou, Xiang; E, Weinan
2010
Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model. Zbl 1277.81117
E, Weinan; Lu, Jianfeng
2010
Localized bases of eigensubspaces and operator compression. Zbl 1205.15017
E, Weinan; Li, Tiejun; Lu, Jianfeng
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
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
2010
On the crystallization of 2D hexagonal lattices. Zbl 1180.82191
E, Weinan; Li, Dong
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
2009
A general strategy for designing seamless multiscale methods. Zbl 1280.76038
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
2009
Pole-based approximation of the Fermi-Dirac function. Zbl 1188.41007
Lin, Lin; Lu, Jianfeng; Ying, Lexing; Weinan, E.
2009
Orbital minimization with localization. Zbl 1170.46313
Gao, Weiguo; E, Weinan
2009
Effectiveness of implicit methods for stiff stochastic differential equations. Zbl 1199.65010
Li, Tiejun; Abdulle, Assyr; Weinan, E
2008
Optimal partition and effective dynamics of complex networks. Zbl 1205.68031
E, Weinan; Li, Tiejun; Vanden-Eijnden, Eric
2008
The Andersen thermostat in molecular dynamics. Zbl 1148.82019
E, Weinan; Li, Dong
2008
Breakdown of homogenization for the random Hamilton-Jacobi equations. Zbl 1207.70018
E, Weinan; Wehr, Jan; Xin, Jack
2008
Heterogeneous multiscale methods: a review. Zbl 1164.65496
E, Weinan; Engquist, Bjorn; Li, Xiantao; Ren, Weiqing; Vanden-Eijnden, Eric
2007
Cauchy-Born rule and the stability of crystalline solids: Static problems. Zbl 1106.74019
E, Weinan; Ming, Pingbing
2007
Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales. Zbl 1162.80003
E, Weinan; Liu, Di; Vanden-Eijnden, Eric
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
2007
Boundary conditions for the moving contact line problem. Zbl 1146.76513
Ren, Weiqing; E, Weinan
2007
Cauchy-Born rule and the stability of crystalline solids: dynamic problems. Zbl 1138.35063
E, Weinan; Ming, Pingbing
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
2007
The elastic continuum limit of the tight binding model. Zbl 1136.74003
E, Weinan; Lu, Jianfeng
2007
A sub-linear scaling algorithm for computing the electronic structure of materials. Zbl 1133.35429
García-Cervera, Carlos J.; Lu, Jianfeng; E, Weinan
2007
Seamless multiscale modeling via dynamics on fiber bundles. Zbl 1133.65029
E, Weinan; Lu, Jianfeng
2007
Towards a theory of transition paths. Zbl 1101.82016
E, Weinan; Vanden-Eijnden, Eric
2006
Variational boundary conditions for molecular dynamics simulations of solids at low temperature. Zbl 1114.74326
Li, Xiantao; E, Weinan
2006
A molecular kinetic theory of inhomogeneous liquid crystal flow and the small Deborah number limit. Zbl 1131.76010
E, Weinan; Zhang, Pingwen
2006
Simulations of 3-D domain wall structures in thin films. Zbl 1099.35153
Wang, Xiao-Ping; Wang, Ke; E, Weinan
2006
Analysis of the heterogeneous multiscale method for elliptic homogenization problems. Zbl 1060.65118
E, Weinan; Ming, Pingbing; Zhang, Pingwen
2005
Analysis of multiscale methods for stochastic differential equations. Zbl 1080.60060
E, Weinan; Liu, Di; Vanden-Eijnden, Eric
2005
Multiscale modeling of the dynamics of solids at finite temperature. Zbl 1120.74313
Li, Xiantao; E, Weinan
2005
Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics. Zbl 1143.76541
Ren, Weiqing; E, Weinan
2005
The heterogeneous multi-scale method for homogenization problems. Zbl 1086.65521
E, Weinan; Engquist, Björn
2005
Self-induced stochastic resonance in excitable systems. Zbl 1109.34040
Muratov, Cyrill B.; Vanden-Eijnden, Eric; E, Weinan
2005
Analysis of the local quasicontinuum method. Zbl 1188.74019
E, Weinan; Ming, Pingbing
2005
Numerical methods for multiscale transport equations and application to two-phase porous media flow. Zbl 1089.76049
Yue, Xingye; E, Weinan
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
2005
Minimum action method for the study of rare events. Zbl 1050.60068
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
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.
2004
Well-posedness for the dumbbell model of polymeric fluids. Zbl 1060.35169
E, Weinan; Li, Tiejun; Zhang, Pingwen
2004
Some recent progress in multiscale modeling. Zbl 1419.74252
E, Weinan; Li, Xiantao; Vanden-Eijnden, Eric
2004
Analysis of multiscale methods. Zbl 1046.65108
E, Weinan; Ming, Pingbing
2004
Metastability, conformation dynamics, and transition pathways in complex systems. Zbl 1141.82312
E, Weinan; Vanden-Eijnden, Eric
2004
Stochastic models of polymeric fluids at small Deborah number. Zbl 1078.76009
Li, T.; Vanden-Eijnden, E.; Zhang, P.; E, W.
2004
Analysis of the heterogeneous multiscale method for gas dynamics. Zbl 1177.76355
E, Weinan; Li, Xiantao
2004
The heterogeneous multi-scale method. Zbl 1328.74087
E, Weinan; Engquist, Bjorn
2004
Heterogeneous multiscale method for locally self-similar problems. Zbl 1081.82563
E, Weinan; Yue, Xing Y.
2004
The heterogeneous multiscale methods. Zbl 1093.35012
E, Weinan; Engquist, Bjorn
2003
Gauge method for viscous incompressible flows. Zbl 1160.76329
E, Weinan; Liu, Jian-Guo
2003
Multiscale modeling and computation. Zbl 1032.65013
E, Weinan; Engquist, Bjorn
2003
Finite difference heterogeneous multi-scale method for homogenization problems. Zbl 1034.65067
Abdulle, Assyr; E, Weinan
2003
Analysis of the heterogeneous multiscale method for ordinary differential equations. Zbl 1088.65552
E, Weinan
2003
Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth. Zbl 1023.82007
Schulze, Tim P.; Smereka, Peter; E, Weinan
2003
A note on generalized flows. Zbl 1042.34009
E, Weinan; Vanden-Eijnden, Eric
2003
Accurate numerical methods for micromagnetics simulations with general geometries. Zbl 1036.78016
García-Cervera, Carlos J.; Gimbutas, Zydrunas; E, Weinan
2003
A dynamic atomistic–continuum method for the simulation of crystalline materials. Zbl 1013.82022
E, Weinan; Huang, Zhongyi
2002
Energy landscapes and rare events. Zbl 1023.65004
E, Weinan; Ren, Weiqing; Vanden-Eijnden, Eric
2002
Projection method. III: Spatial discretization on the staggered grid. Zbl 1058.76043
E, Weinan; Liu, Jian-Guo
2002
Gibbsian dynamics and invariant measures for stochastic dissipative PDEs. Zbl 1023.60057
E, Weinan; Liu, Di
2002
Convergence of a stochastic method for the modeling of polymeric fluids. Zbl 1137.76313
E, Weinan; Li, Tiejun; Zhang, Pingwen
2002
...and 54 more Documents
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#### 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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