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ORCIDWeinan E
鄂维南;
Person information
- unicode name: 鄂维南;
- affiliation: Beijing Institute of Big Data Research, China
- affiliation: Princeton University, Department of Mathematics, NJ, USA
- affiliation: Peking University, China
- award: Presidential Early Career Award for Scientists and Engineers
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2020 – today
- 2024
[i74]Zhi-Qin John Xu, Junjie Yao, Yuxiao Yi, Liangkai Hang, Weinan E, Yaoyu Zhang, Tianhan Zhang:
Solving multiscale dynamical systems by deep learning. CoRR abs/2401.01220 (2024)- [i73]Zhongwang Zhang, Zhiwei Wang, Junjie Yao, Zhangchen Zhou, Xiaolong Li, Weinan E, Zhi-Qin John Xu:
Anchor function: a type of benchmark functions for studying language models. CoRR abs/2401.08309 (2024) - [i72]Mingze Wang, Weinan E:
Understanding the Expressive Power and Mechanisms of Transformer for Sequence Modeling. CoRR abs/2402.00522 (2024) - [i71]Pinchen Xie, Yunrui Qiu, Weinan E:
Coarse-graining conformational dynamics with multi-dimensional generalized Langevin equation: how, when, and why. CoRR abs/2405.12356 (2024) - [i70]Mingze Wang, Haotian He, Jinbo Wang, Zilin Wang, Guanhua Huang, Feiyu Xiong, Zhiyu Li, Weinan E, Lei Wu:
Improving Generalization and Convergence by Enhancing Implicit Regularization. CoRR abs/2405.20763 (2024) - [i69]Xiaohong Ji, Zhen Wang, Zhifeng Gao, Hang Zheng, Linfeng Zhang, Guolin Ke, Weinan E:
Uni-Mol2: Exploring Molecular Pretraining Model at Scale. CoRR abs/2406.14969 (2024) - [i68]Hongkang Yang, Zehao Lin, Wenjin Wang, Hao Wu, Zhiyu Li, Bo Tang, Wenqiang Wei, Jinbo Wang, Zeyun Tang, Shichao Song
, Chenyang Xi, Yu Yu, Kai Chen, Feiyu Xiong, Linpeng Tang, Weinan E:
Memory3: Language Modeling with Explicit Memory. CoRR abs/2407.01178 (2024) - [i67]Boshen Zeng, Sian Chen, Xinxin Liu, Changhong Chen, Bin Deng, Xiaoxu Wang, Zhifeng Gao, Yuzhi Zhang, Weinan E, Linfeng Zhang:
Uni-ELF: A Multi-Level Representation Learning Framework for Electrolyte Formulation Design. CoRR abs/2407.06152 (2024) - [i66]Mingze Wang, Ruoxi Yu, Weinan E, Lei Wu:
How Transformers Implement Induction Heads: Approximation and Optimization Analysis. CoRR abs/2410.11474 (2024) - 2023
- [b1]Gaoyan Ou, Zhanxing Zhu, Bin Dong, Weinan E, Binyang Li, Shumin Shi:
Introduction to Data Science. WorldScientific 2023, ISBN 9789811263897, pp. 1-444 - [j31]Yixiao Chen, Linfeng Zhang, Han Wang, Weinan E:
DeePKS-kit: A package for developing machine learning-based chemically accurate energy and density functional models. Comput. Phys. Commun. 282: 108520 (2023) - [c19]Guanhua Huang, Runxin Xu, Ying Zeng, Jiaze Chen, Zhouwang Yang, Weinan E:
An Iteratively Parallel Generation Method with the Pre-Filling Strategy for Document-level Event Extraction. EMNLP 2023: 10834-10852 - [i65]Zeping Min, Qian Ge, Zhong Li, Weinan E:
AMP: A unified framework boosting low resource automatic speech recognition. CoRR abs/2302.03498 (2023) - [i64]Jingrun Chen, Weinan E, Yixin Luo:
The Random Feature Method for Time-dependent Problems. CoRR abs/2304.06913 (2023) - [i63]Jun Zhang, Xiaohan Lin, Weinan E, Yi Qin Gao:
Machine-Learned Invertible Coarse Graining for Multiscale Molecular Modeling. CoRR abs/2305.01243 (2023) - [i62]Wei Hu, Yue Zhao, Weinan E, Jiequn Han, Jihao Long:
Learning Free Terminal Time Optimal Closed-loop Control of Manipulators. CoRR abs/2311.17749 (2023) - 2022
- [j30]Zhong Li, Jiequn Han, Weinan E, Qianxiao Li:
Approximation and Optimization Theory for Linear Continuous-Time Recurrent Neural Networks. J. Mach. Learn. Res. 23: 42:1-42:85 (2022) - [j29]Dongdong Wang, Yanze Wang, Junhan Chang, Linfeng Zhang, Han Wang, Weinan E:
Efficient sampling of high-dimensional free energy landscapes using adaptive reinforced dynamics. Nat. Comput. Sci. 2(1): 20-29 (2022) - [j28]Weinan E, Yajun Zhou:
A Mathematical Model for Universal Semantics. IEEE Trans. Pattern Anal. Mach. Intell. 44(3): 1124-1132 (2022) - [c18]Yaohua Zang, Jihao Long, Xuanxi Zhang, Wei Hu, Weinan E, Jiequn Han:
A Machine Learning Enhanced Algorithm for the Optimal Landing Problem. MSML 2022: 319-334 - [i61]Zhiwei Wang, Yaoyu Zhang, Yiguang Ju, Weinan E, Zhi-Qin John Xu, Tianhan Zhang:
A deep learning-based model reduction (DeePMR) method for simplifying chemical kinetics. CoRR abs/2201.02025 (2022) - [i60]Tianhan Zhang, Yuxiao Yi, Yifan Xu, Zhi X. Chen, Yaoyu Zhang, Weinan E, Zhi-Qin John Xu:
A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics. CoRR abs/2201.03549 (2022) - [i59]Jingrun Chen, Xurong Chi, Weinan E, Zhouwang Yang:
Bridging Traditional and Machine Learning-based Algorithms for Solving PDEs: The Random Feature Method. CoRR abs/2207.13380 (2022) - 2021
- [j27]Denghui Lu, Han Wang, Mohan Chen, Lin Lin, Roberto Car, Weinan E, Weile Jia, Linfeng Zhang:
86 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracy. Comput. Phys. Commun. 259: 107624 (2021) - [c17]Zhong Li, Jiequn Han, Weinan E, Qianxiao Li:
On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis. ICLR 2021 - [c16]Weinan E, Stephan Wojtowytsch:
Some observations on high-dimensional partial differential equations with Barron data. MSML 2021: 253-269 - [c15]Weinan E, Stephan Wojtowytsch:
On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers. MSML 2021: 270-290 - [c14]Chao Ma, Lei Wu, Weinan E:
A Qualitative Study of the Dynamic Behavior for Adaptive Gradient Algorithms. MSML 2021: 671-692 - [c13]Hongkang Yang, Weinan E:
Generalization and Memorization: The Bias Potential Model. MSML 2021: 1013-1043 - [i58]Jihao Long, Jiequn Han, Weinan E:
An L2 Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation. CoRR abs/2104.07794 (2021) - [i57]Hongkang Yang, Weinan E:
Generalization Error of GAN from the Discriminator's Perspective. CoRR abs/2107.03633 (2021) - [i56]Jiequn Han, Yucheng Yang, Weinan E:
DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks. CoRR abs/2112.14377 (2021) - [i55]Lidong Fang, Pei Ge, Lei Zhang, Huan Lei, Weinan E:
DeePN2: A deep learning-based non-Newtonian hydrodynamic model. CoRR abs/2112.14798 (2021) - 2020
- [j26]Yuzhi Zhang, Haidi Wang, Weijie Chen, Jinzhe Zeng, Linfeng Zhang, Han Wang, Weinan E:
DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models. Comput. Phys. Commun. 253: 107206 (2020) - [j25]Stephan Wojtowytsch, Weinan E:
Can Shallow Neural Networks Beat the Curse of Dimensionality? A Mean Field Training Perspective. IEEE Trans. Artif. Intell. 1(2): 121-129 (2020) - [c12]Zehao Don, Weinan E, Chao Ma:
A Priori Estimates of the Generalization Error for Autoencoders. ICASSP 2020: 3327-3331 - [c11]Chao Ma, Lei Wu, Weinan E:
The Slow Deterioration of the Generalization Error of the Random Feature Model. MSML 2020: 373-389 - [c10]Pan Zhou, Jiashi Feng, Chao Ma, Caiming Xiong, Steven Chu-Hong Hoi, Weinan E:
Towards Theoretically Understanding Why Sgd Generalizes Better Than Adam in Deep Learning. NeurIPS 2020 - [c9]Weile Jia, Han Wang, Mohan Chen, Denghui Lu, Lin Lin, Roberto Car, Weinan E, Linfeng Zhang:
Pushing the limit of molecular dynamics with ab initio accuracy to 100 million atoms with machine learning. SC 2020: 5 - [i54]Huan Lei, Lei Wu, Weinan E:
Machine learning based non-Newtonian fluid model with molecular fidelity. CoRR abs/2003.03672 (2020) - [i53]Denghui Lu, Han Wang, Mohan Chen, Jiduan Liu, Lin Lin, Roberto Car, Weinan E, Weile Jia, Linfeng Zhang:
86 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracy. CoRR abs/2004.11658 (2020) - [i52]Weinan E, Stephan Wojtowytsch:
Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels. CoRR abs/2005.10807 (2020) - [i51]Stephan Wojtowytsch, Weinan E:
Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective. CoRR abs/2005.10815 (2020) - [i50]Weinan E, Jiequn Han, Linfeng Zhang:
Integrating Machine Learning with Physics-Based Modeling. CoRR abs/2006.02619 (2020) - [i49]Weinan E, Stephan Wojtowytsch:
Representation formulas and pointwise properties for Barron functions. CoRR abs/2006.05982 (2020) - [i48]Chao Ma, Lei Wu, Weinan E:
The Quenching-Activation Behavior of the Gradient Descent Dynamics for Two-layer Neural Network Models. CoRR abs/2006.14450 (2020) - [i47]Pinchen Xie, Weinan E:
Coarse-grained spectral projection (CGSP): A scalable and parallelizable deep learning-based approach to quantum unitary dynamics. CoRR abs/2007.09788 (2020) - [i46]Weinan E, Stephan Wojtowytsch:
On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics. CoRR abs/2007.15623 (2020) - [i45]Yixiao Chen, Linfeng Zhang, Han Wang, Weinan E:
DeePKS: a comprehensive data-driven approach towards chemically accurate density functional theory. CoRR abs/2008.00167 (2020) - [i44]Chao Ma, Lei Wu, Weinan E:
The Slow Deterioration of the Generalization Error of the Random Feature Model. CoRR abs/2008.05621 (2020) - [i43]Weinan E, Jiequn Han, Arnulf Jentzen:
Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning. CoRR abs/2008.13333 (2020) - [i42]Haijun Yu, Xinyuan Tian, Weinan E, Qianxiao Li:
OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle. CoRR abs/2009.02327 (2020) - [i41]Chao Ma, Lei Wu, Weinan E:
A Qualitative Study of the Dynamic Behavior of Adaptive Gradient Algorithms. CoRR abs/2009.06125 (2020) - [i40]Zhong Li, Jiequn Han, Weinan E, Qianxiao Li:
On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis. CoRR abs/2009.07799 (2020) - [i39]Weinan E, Chao Ma, Stephan Wojtowytsch, Lei Wu:
Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't. CoRR abs/2009.10713 (2020) - [i38]Weinan E, Stephan Wojtowytsch:
A priori estimates for classification problems using neural networks. CoRR abs/2009.13500 (2020) - [i37]Weinan E:
Machine Learning and Computational Mathematics. CoRR abs/2009.14596 (2020) - [i36]Yucheng Yang, Yue Pang, Guanhua Huang, Weinan E:
The Knowledge Graph for Macroeconomic Analysis with Alternative Big Data. CoRR abs/2010.05172 (2020) - [i35]Yucheng Yang, Zhong Zheng, Weinan E:
Interpretable Neural Networks for Panel Data Analysis in Economics. CoRR abs/2010.05311 (2020) - [i34]Pan Zhou, Jiashi Feng, Chao Ma, Caiming Xiong, Steven C. H. Hoi, Weinan E:
Towards Theoretically Understanding Why SGD Generalizes Better Than ADAM in Deep Learning. CoRR abs/2010.05627 (2020) - [i33]Hongkang Yang, Weinan E:
Generalization and Memorization: The Bias Potential Model. CoRR abs/2011.14269 (2020) - [i32]Weinan E, Stephan Wojtowytsch:
Some observations on partial differential equations in Barron and multi-layer spaces. CoRR abs/2012.01484 (2020) - [i31]Weinan E, Stephan Wojtowytsch:
On the emergence of tetrahedral symmetry in the final and penultimate layers of neural network classifiers. CoRR abs/2012.05420 (2020) - [i30]Tianhan Zhang, Yaoyu Zhang, Weinan E, Yiguang Ju:
A deep learning-based ODE solver for chemical kinetics. CoRR abs/2012.12654 (2020)
2010 – 2019
- 2019
- [j24]Jiequn Han, Linfeng Zhang, Weinan E:
Solving many-electron Schrödinger equation using deep neural networks. J. Comput. Phys. 399 (2019) - [j23]Qianxiao Li, Cheng Tai, Weinan E:
Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations. J. Mach. Learn. Res. 20: 40:1-40:47 (2019) - [j22]Christian Beck, Weinan E, Arnulf Jentzen:
Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations. J. Nonlinear Sci. 29(4): 1563-1619 (2019) - [j21]Weinan E, Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse:
On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations. J. Sci. Comput. 79(3): 1534-1571 (2019) - [i29]Weinan E, Chao Ma, Qingcan Wang:
A Priori Estimates of the Population Risk for Residual Networks. CoRR abs/1903.02154 (2019) - [i28]Weinan E, Chao Ma, Lei Wu:
A Comparative Analysis of the Optimization and Generalization Property of Two-layer Neural Network and Random Feature Models Under Gradient Descent Dynamics. CoRR abs/1904.04326 (2019) - [i27]Weinan E, Chao Ma, Qingcan Wang, Lei Wu:
Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections. CoRR abs/1904.05263 (2019) - [i26]Weinan E, Chao Ma, Lei Wu:
Barron Spaces and the Compositional Function Spaces for Neural Network Models. CoRR abs/1906.08039 (2019) - [i25]Weinan E, Yajun Zhou:
A Mathematical Model for Linguistic Universals. CoRR abs/1907.12293 (2019) - [i24]Weinan E, Chao Ma, Lei Wu:
On the Generalization Properties of Minimum-norm Solutions for Over-parameterized Neural Network Models. CoRR abs/1912.06987 (2019) - [i23]Weinan E, Chao Ma, Lei Wu:
Machine Learning from a Continuous Viewpoint. CoRR abs/1912.12777 (2019) - 2018
- [j20]Han Wang, Linfeng Zhang, Jiequn Han, Weinan E:
DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics. Comput. Phys. Commun. 228: 178-184 (2018) - [c8]Linfeng Zhang, Jiequn Han, Han Wang, Wissam Saidi, Roberto Car, Weinan E:
End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems. NeurIPS 2018: 4441-4451 - [c7]Lei Wu, Chao Ma, Weinan E:
How SGD Selects the Global Minima in Over-parameterized Learning: A Dynamical Stability Perspective. NeurIPS 2018: 8289-8298 - [i22]Lei Wu, Zhanxing Zhu, Cheng Tai, Weinan E:
Understanding and Enhancing the Transferability of Adversarial Examples. CoRR abs/1802.09707 (2018) - [i21]Weinan E, Qingcan Wang:
Exponential Convergence of the Deep Neural Network Approximation for Analytic Functions. CoRR abs/1807.00297 (2018) - [i20]Weinan E, Jiequn Han, Qianxiao Li:
A Mean-Field Optimal Control Formulation of Deep Learning. CoRR abs/1807.01083 (2018) - [i19]Chao Ma, Jianchun Wang, Weinan E:
Model Reduction with Memory and the Machine Learning of Dynamical Systems. CoRR abs/1808.04258 (2018) - [i18]Linfeng Zhang, Weinan E, Lei Wang:
Monge-Ampère Flow for Generative Modeling. CoRR abs/1809.10188 (2018) - [i17]Weinan E, Chao Ma, Lei Wu:
A Priori Estimates of the Generalization Error for Two-layer Neural Networks. CoRR abs/1810.06397 (2018) - [i16]Linfeng Zhang, De-Ye Lin, Han Wang, Roberto Car, Weinan E:
Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulation. CoRR abs/1810.11890 (2018) - [i15]Qianxiao Li, Cheng Tai, Weinan E:
Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations. CoRR abs/1811.01558 (2018) - 2017
- [j19]Qianxiao Li, Long Chen, Cheng Tai, Weinan E:
Maximum Principle Based Algorithms for Deep Learning. J. Mach. Learn. Res. 18: 165:1-165:29 (2017) - [c6]Qianxiao Li, Cheng Tai, Weinan E:
Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms. ICML 2017: 2101-2110 - [c5]Rui Yan, Dongyan Zhao, Weinan E:
Joint Learning of Response Ranking and Next Utterance Suggestion in Human-Computer Conversation System. SIGIR 2017: 685-694 - [i14]Weinan E, Jiequn Han, Arnulf Jentzen:
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. CoRR abs/1706.04702 (2017) - [i13]Lei Wu, Zhanxing Zhu, Weinan E:
Towards Understanding Generalization of Deep Learning: Perspective of Loss Landscapes. CoRR abs/1706.10239 (2017) - [i12]Jiequn Han, Arnulf Jentzen, Weinan E:
Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning. CoRR abs/1707.02568 (2017) - [i11]Linfeng Zhang, Jiequn Han, Han Wang, Roberto Car, Weinan E:
Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics. CoRR abs/1707.09571 (2017) - [i10]Christian Beck, Weinan E, Arnulf Jentzen:
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. CoRR abs/1709.05963 (2017) - [i9]Weinan E, Bing Yu:
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems. CoRR abs/1710.00211 (2017) - [i8]Qianxiao Li, Long Chen, Cheng Tai, Weinan E:
Maximum Principle Based Algorithms for Deep Learning. CoRR abs/1710.09513 (2017) - [i7]Linfeng Zhang, Han Wang, Weinan E:
Reinforced dynamics for enhanced sampling in large atomic and molecular systems. I. Basic Methodology. CoRR abs/1712.03461 (2017) - [i6]Han Wang, Linfeng Zhang, Jiequn Han, Weinan E:
DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics. CoRR abs/1712.03641 (2017) - 2016
- [j18]Cheng Tai, Weinan E:
Multiscale Adaptive Representation of Signals: I. The Basic Framework. J. Mach. Learn. Res. 17: 140:1-140:38 (2016) - [c4]Chu Wang, Qianxiao Li, Weinan E, Bernard Chazelle:
Noisy Hegselmann-Krause systems: Phase transition and the 2R-conjecture. CDC 2016: 2632-2637 - [c3]Cheng Tai, Tong Xiao, Xiaogang Wang, Weinan E:
Convolutional neural networks with low-rank regularization. ICLR (Poster) 2016 - [i5]Jiequn Han, Weinan E:
Deep Learning Approximation for Stochastic Control Problems. CoRR abs/1611.07422 (2016) - 2015
- [i4]Cheng Tai, Weinan E:
Multiscale Adaptive Representation of Signals: I. The Basic Framework. CoRR abs/1507.04835 (2015) - [i3]Chu Wang, Yingfei Wang, Weinan E, Robert E. Schapire:
Functional Frank-Wolfe Boosting for General Loss Functions. CoRR abs/1510.02558 (2015) - [i2]Qianxiao Li, Cheng Tai, Weinan E:
Dynamics of Stochastic Gradient Algorithms. CoRR abs/1511.06251 (2015) - 2014
- [c2]Haoshu Tian, Weinan E:
Fire sale in financial networks. CISS 2014: 1-5 - 2013
- [j17]Lin Lin, Sihong Shao, Weinan E:
Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory. J. Comput. Phys. 245: 205-217 (2013) - 2012
- [j16]Assyr Abdulle, Weinan E, Björn Engquist, Eric Vanden-Eijnden:
The heterogeneous multiscale method. Acta Numer. 21: 1-87 (2012) - [j15]Lin Lin, Jianfeng Lu, Lexing Ying, Weinan E:
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation. J. Comput. Phys. 231(4): 2140-2154 (2012) - [j14]Lin Lin, Jianfeng Lu, Lexing Ying, Weinan E:
Optimized local basis set for Kohn-Sham density functional theory. J. Comput. Phys. 231(13): 4515-4529 (2012) - [i1]Weinan E, Jianfeng Lu, Yuan Yao:
The Landscape of Complex Networks. CoRR abs/1204.6376 (2012) - 2011
- [j13]Weinan E, Jianfeng Lu:
Multiscale modeling. Scholarpedia 6(10): 11527 (2011) - [j12]Lin Lin, Chao Yang, Jianfeng Lu, Lexing Ying, Weinan E:
A Fast Parallel Algorithm for Selected Inversion of Structured Sparse Matrices with Application to 2D Electronic Structure Calculations. SIAM J. Sci. Comput. 33(3): 1329-1351 (2011) - [j11]Lin Lin, Chao Yang, Juan C. Meza, Jianfeng Lu, Lexing Ying, Weinan E:
SelInv - An Algorithm for Selected Inversion of a Sparse Symmetric Matrix. ACM Trans. Math. Softw. 37(4): 40:1-40:19 (2011) - [c1]Jingchen Liu, Rohit Patra, Xiang Zhou, Weinan E:
Failure of random materials: a large deviation and computational study. WSC 2011: 3784-3794 - 2010
- [j10]Ling Lin, Xiuyuan Cheng, Weinan E, An-Chang Shi, Pingwen Zhang:
A numerical method for the study of nucleation of ordered phases. J. Comput. Phys. 229(5): 1797-1809 (2010) - [j9]Xiantao Li, Jerry Zhijian Yang, Weinan E:
A multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks. J. Comput. Phys. 229(10): 3970-3987 (2010)
2000 – 2009
- 2009
- [j8]Weinan E, Weiqing Ren, Eric Vanden-Eijnden:
A general strategy for designing seamless multiscale methods. J. Comput. Phys. 228(15): 5437-5453 (2009) - 2007
- [j7]Weinan E, Di Liu, Eric Vanden-Eijnden:
Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales. J. Comput. Phys. 221(1): 158-180 (2007) - [j6]Xingye Yue, Weinan E:
The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size. J. Comput. Phys. 222(2): 556-572 (2007) - [j5]Shanqin Chen, Weinan E, Yunxian Liu, Chi-Wang Shu:
A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations. J. Comput. Phys. 225(2): 1314-1330 (2007) - 2005
- [j4]Shanqin Chen, Weinan E, Chi-Wang Shu:
The Heterogeneous Multiscale Method Based on the Discontinuous Galerkin Method for Hyperbolic and Parabolic Problems. Multiscale Model. Simul. 3(4): 871-894 (2005) - 2002
- [j3]Weinan E, Jian-Guo Liu:
Projection method III: Spatial discretization on the staggered grid. Math. Comput. 71(237): 27-47 (2002) - 2001
- [j2]Jian-Guo Liu, Weinan E:
Simple finite element method in vorticity formulation for incompressible flows. Math. Comput. 70(234): 579-593 (2001) - 2000
- [j1]Weinan E, Xiao-Ping Wang:
Numerical Methods for the Landau-Lifshitz Equation. SIAM J. Numer. Anal. 38(5): 1647-1665 (2000)
Coauthor Index
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