E Weinan

发表

Towards Understanding Generalization of Deep Learning: Perspective of Loss Landscapes pdf

Zhanxing Zhu, E Weinan, Lei Wu, 2017, ArXiv.

Some observations on partial differential equations in Barron and multi-layer spaces pdf

E Weinan, Stephan Wojtowytsch, 2020, ArXiv.

The Slow Deterioration of the Generalization Error of the Random Feature Model

E Weinan, Lei Wu, Chao Ma, 2020, MSML.

Reinforced dynamics of large atomic and molecular systems

E Weinan, Han Wang, Linfeng Zhang, 2017 .

The Heterogeneous Multiscale Method Based on the Discontinuous Galerkin Method for Hyperbolic and Parabolic Problems

E Weinan, Chi-Wang Shu, Shanqin Chen, 2005, Multiscale Model. Simul..

Failure of random materials: A large deviation and computational study

Xiang Zhou, E Weinan, Jingchen Liu, 2011, Proceedings of the 2011 Winter Simulation Conference (WSC).

Multiscale Modeling Of Crystalline Solids

E Weinan, Xiantao Li, 2005 .

Simple finite element method in vorticity formulation for incompressible flows

E Weinan, Jian-Guo Liu, 2001, Math. Comput..

The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems

E Weinan, Bing Yu, E. Weinan, 2017, Communications in Mathematics and Statistics.

The Heterogeneous Multi-Scale Method

E Weinan, Bjorn Engquist, 2002 .

Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections pdf

Lei Wu, E Weinan, Chao Ma, 2019, ArXiv.

A multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks

E Weinan, Xiantao Li, Jerry Z. Yang, 2010, J. Comput. Phys..

Dynamics of Stochastic Gradient Algorithms pdf

E Weinan, Cheng Tai, Qianxiao Li, 2015, ArXiv.

Maximum Principle Based Algorithms for Deep Learning pdf

Long Chen, E Weinan, Cheng Tai, 2017, J. Mach. Learn. Res..

On the Generalization Properties of Minimum-norm Solutions for Over-parameterized Neural Network Models pdf

E Weinan, Chao Ma, Lei Wu, 2019, ArXiv.

A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics

Lei Wu, E Weinan, Chao Ma, 2019, Science China Mathematics.

DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics pdf

E Weinan, Han Wang, Linfeng Zhang, 2017, Comput. Phys. Commun..

Towards Theoretically Understanding Why SGD Generalizes Better Than ADAM in Deep Learning pdf

E Weinan, Pan Zhou, Jiashi Feng, 2020, NeurIPS.

Projection method III: Spatial discretization on the staggered grid

E Weinan, Jian-Guo Liu, Jian‐Guo Liu, 2002, Math. Comput..

Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulation pdf

E Weinan, Han Wang, Linfeng Zhang, 2018, Physical Review Materials.

Noisy Hegselmann-Krause system: phase transition and 2-R conjecture

Bernard Chazelle, E Weinan, Chu Wang, 2015 .

Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms

E Weinan, Cheng Tai, Qianxiao Li, 2015, ICML.

OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle pdf

E Weinan, Haijun Yu, Qianxiao Li, 2020, ArXiv.

Active Learning of Uniformly Accurate Deep Potential Models for Multicomponent Systems

E Weinan, Han Wang, Linfeng Zhang, 2019 .

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

E Weinan, Arnulf Jentzen, Christian Beck, 2017, J. Nonlinear Sci..

Generalization and Memorization: The Bias Potential Model pdf

E Weinan, Hongkang Yang, 2020, ArXiv.

Multiscale Adaptive Representation of Signals: I. The Basic Framework

E Weinan, Cheng Tai, W. E, 2015, J. Mach. Learn. Res..

Exponential convergence of the deep neural network approximation for analytic functions

E Weinan, Qingcan Wang, W. E, 2018, Science China Mathematics.

The heterogeneous multi-scale method for homogenization problems

E Weinan, Björn Engquist, B. Engquist, 2005 .

Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations

E Weinan, Cheng Tai, Qianxiao Li, 2018, J. Mach. Learn. Res..

Reinforced dynamics for enhanced sampling in large atomic and molecular systems. I. Basic Methodology

E Weinan, Han Wang, Linfeng Zhang, 2017, The Journal of chemical physics.

Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales

E Weinan, Di Liu, Eric Vanden-Eijnden, 2007, J. Comput. Phys..

Barron Spaces and the Compositional Function Spaces for Neural Network Models pdf

Lei Wu, E Weinan, Chao Ma, 2019, ArXiv.

Can Shallow Neural Networks Beat the Curse of Dimensionality? A Mean Field Training Perspective pdf

E Weinan, Stephan Wojtowytsch, E. Weinan, 2020, IEEE Transactions on Artificial Intelligence.

Numerical Methods for the Landau-Lifshitz Equation

E Weinan, Xiao-Ping Wang, E. Weinan, 2000, SIAM J. Numer. Anal..

Understanding and Enhancing the Transferability of Adversarial Examples pdf

Lei Wu, Zhanxing Zhu, E Weinan, 2018, ArXiv.

Optimized local basis set for Kohn-Sham density functional theory

E Weinan, Lexing Ying, Lin Lin, 2011, J. Comput. Phys..

On Multilevel Picard Numerical Approximations for High-Dimensional Nonlinear Parabolic Partial Differential Equations and High-Dimensional Nonlinear Backward Stochastic Differential Equations

E Weinan, Arnulf Jentzen, Thomas Kruse, 2017, Journal of Scientific Computing.

Fire sale in financial networks

E Weinan, Haoshu Tian, 2014, 2014 48th Annual Conference on Information Sciences and Systems (CISS).

Representation formulas and pointwise properties for Barron functions pdf

E Weinan, Stephan Wojtowytsch, 2020, ArXiv.

A Fast Parallel Algorithm for Selected Inversion of Structured Sparse Matrices with Application to 2D Electronic Structure Calculations

E Weinan, Lexing Ying, Chao Yang, 2010, SIAM J. Sci. Comput..

Deep Learning Approximation for Stochastic Control Problems pdf

E Weinan, Jiequn Han, W. E, 2016, ArXiv.

The Landscape of Complex Networks pdf

Yuan Yao, E Weinan, Jianfeng Lu, 2012, ArXiv.

Kolmogorov width decay and poor approximators in machine learning: shallow neural networks, random feature models and neural tangent kernels

E Weinan, Stephan Wojtowytsch, E. Weinan, 2020, ArXiv.

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

E Weinan, Arnulf Jentzen, Jiequn Han, 2017, Communications in Mathematics and Statistics.

A Qualitative Study of the Dynamic Behavior of Adaptive Gradient Algorithms pdf

E Weinan, Lei Wu, Chao Ma, 2020, ArXiv.

86 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracy pdf

E Weinan, Weile Jia, Lin Lin, 2020, Comput. Phys. Commun..

Seamless multiscale modeling via dynamics on fiber bundles

E Weinan, Jianfeng Lu, E. Weinan, 2007 .

Monge-Ampère Flow for Generative Modeling pdf

E Weinan, Lei Wang, Linfeng Zhang, 2018, ArXiv.

Multi-scale Modeling and Computation

E Weinan, Björn Engquist, B. Engquist, 2003 .

Integrating Machine Learning with Physics-Based Modeling pdf

E Weinan, Linfeng Zhang, Jiequn Han, 2020, ArXiv.

Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning pdf

E Weinan, Arnulf Jentzen, Jiequn Han, 2017, ArXiv.

Model Reduction with Memory and the Machine Learning of Dynamical Systems pdf

E Weinan, Jianchun Wang, Chao Ma, 2018, Communications in Computational Physics.

On the emergence of tetrahedral symmetry in the final and penultimate layers of neural network classifiers pdf

E Weinan, Stephan Wojtowytsch, 2020, ArXiv.

Heterogeneous multiscale method: A general methodology for multiscale modeling

E Weinan, Zhongyi Huang, Björn Engquist, 2003 .

Multiscale modeling

E Weinan, Jianfeng Lu, E. Weinan, 2019, Scholarpedia.

Coarse-grained spectral projection: A deep learning assisted approach to quantum unitary dynamics

E Weinan, Pinchen Xie, W. E, 2021 .

A discontinuous Galerkin implementation of a domain decomposition method for kinetic-hydrodynamic coupling multiscale problems in gas dynamics and device simulations

E Weinan, Chi-Wang Shu, Yunxian Liu, 2007, J. Comput. Phys..

How SGD Selects the Global Minima in Over-parameterized Learning: A Dynamical Stability Perspective

Lei Wu, E Weinan, Chao Ma, 2018, NeurIPS.

Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics

E Weinan, Han Wang, Linfeng Zhang, 2017, Physical review letters.

Noisy Hegselmann-Krause Systems: Phase Transition and the 2R-Conjecture

Bernard Chazelle, E Weinan, Chu Wang, 2015, 2016 IEEE 55th Conference on Decision and Control (CDC).

End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems

E Weinan, Han Wang, Linfeng Zhang, 2018, NeurIPS.

Functional Frank-Wolfe Boosting for General Loss Functions pdf

E Weinan, Robert E. Schapire, Chu Wang, 2015, ArXiv.

The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size

E Weinan, Xingye Yue, E. Weinan, 2007, J. Comput. Phys..

A Priori Estimates of the Generalization Error for Two-layer Neural Networks pdf

Lei Wu, E Weinan, Chao Ma, 2018, Communications in Mathematical Sciences.

A mean-field optimal control formulation of deep learning

E Weinan, Qianxiao Li, Jiequn Han, 2018, Research in the Mathematical Sciences.

Machine learning based non-Newtonian fluid model with molecular fidelity

E Weinan, Lei Wu, Huan Lei, 2020, Physical review. E.

The Heterognous Multiscale Methods

E Weinan, Björn Engquist, W. E, 2003 .

A numerical method for the study of nucleation of ordered phases

E Weinan, Ling Lin, Pingwen Zhang, 2010, J. Comput. Phys..

A deep learning-based ODE solver for chemical kinetics pdf

E Weinan, Yaoyu Zhang, Yiguang Ju, 2020, ArXiv.

Solving many-electron Schrödinger equation using deep neural networks

E Weinan, Linfeng Zhang, Jiequn Han, 2018, J. Comput. Phys..

Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory

Sihong Shao, E Weinan, Lin Lin, 2012, J. Comput. Phys..

The Quenching-Activation Behavior of the Gradient Descent Dynamics for Two-layer Neural Network Models pdf

E Weinan, Lei Wu, Chao Ma, 2020, ArXiv.

Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation

E Weinan, Lexing Ying, Lin Lin, 2011, J. Comput. Phys..

The Barron Space and the Flow-Induced Function Spaces for Neural Network Models

E Weinan, Chao Ma, Lei Wu, 2021, Constructive Approximation.

An L2 Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation pdf

E Weinan, Jiequn Han, Jihao Long, 2021, ArXiv.

DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks pdf

E Weinan, Jiequn Han, Yucheng Yang, 2021, SSRN Electronic Journal.

An Expectation-Maximization Algorithm for Continuous-time Hidden Markov Models

E Weinan, Qingcan Wang, E. Weinan, 2021, 2103.16810.

A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics pdf

E Weinan, Tianhan Zhang, Yuxiao Yi, 2022, ArXiv.

On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis pdf

E Weinan, Qianxiao Li, Jiequn Han, 2020, ICLR.

A deep learning-based model reduction (DeePMR) method for simplifying chemical kinetics pdf

E Weinan, Yiguang Ju, Tianhan Zhang, 2022, ArXiv.

DeePN2: A deep learning-based non-Newtonian hydrodynamic model pdf

E Weinan, Lei Zhang, Huan Lei, 2021, ArXiv.

Generalization error of GAN from the discriminator’s perspective pdf

E Weinan, Hongkang Yang, W. E, 2021, Research in the Mathematical Sciences.

Numerical methods for multiscale transport equations and application to two-phase porous media flow

E Weinan, Xingye Yue, E. Weinan, 2005 .

Generalized flows, intrinsic stochasticity, and turbulent transport

E Weinan, Eric Vanden Eijnden, E. Weinan, 2000, nlin/0003028.

Heterogenous multiscale method for locally self-similar problems

E Weinan, E. Weinan, Xingye Yue, 2004 .

Projection Method II: Godunov--Ryabenki Analysis

E Weinan, Jian-Guo Liu, Jian‐Guo Liu, 1996 .

Phase separation in incompressible systems

E Weinan, Peter Palffy-Muhoray, 1997 .

Finite difference heterogeneous multi-scale method for homogenization problems

E Weinan, Assyr Abdulle, E. Weinan, 2003 .

Boundary Layer Theory and the Zero-Viscosity Limit of the Navier-Stokes Equation

E Weinan, E. Weinan, 2000 .

Orientational Ratchets and Angular Momentum Balance in the Janossy Effect

E Weinan, Peter Palffy-Muhoray, 1998 .

A level set method for dislocation dynamics

Yang Xiang, E Weinan, Li-Tien Cheng, 2003 .

Probability Distribution Functions for the Random Forced Burgers Equation

E Weinan, Yakov G. Sinai, Konstantin Khanin, 1997 .

A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

E Weinan, Chi-Wang Shu, Chi-Wang Shu, 1992 .

Turbulent Prandtl number effect on passive scalar advection

E Weinan, Eric Vanden-Eijnden, E. Vanden-Eijnden, 2001 .

On full history recursive multilevel Picard approximations and numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations

E Weinan, Arnulf Jentzen, Thomas Kruse, 2016 .

Analytical Solution of Maxwell's Equations in Lossy and Optically Active Crystals

E Weinan, Peter Palffy-Muhoray, E. Weinan, 2000 .

Finite Difference Schemes for Incompressible Flows in the Velocity-Impulse Density Formulation

E Weinan, Jian-Guo Liu, Jian‐Guo Liu, 1997 .

Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity

E Weinan, E. Weinan, 1994 .

A Molecular Kinetic Theory of Inhomogeneous Liquid Crystal Flow and the Small Deborah Number Limit

E Weinan, Pingwen Zhang, E. Weinan, 2006 .

Generalized Cauchy-Born rules for elastic deformation of sheets, plates, and rods: Derivation of continuum models from atomistic models

E Weinan, Jerry Zhijian Yang, E. Weinan, 2006 .

Transition pathways in complex systems: Reaction coordinates, isocommittor surfaces, and transition tubes

E Weinan, Eric Vanden-Eijnden, Weiqing Ren, 2005 .

AUBRY-MATHER THEORY AND PERIODIC SOLUTIONS OF THE FORCED BURGERS EQUATION

E Weinan, W. E, E. Weinan, 1999 .

Analysis of the heterogeneous multiscale method for gas dynamics

E Weinan, Xiantao Li, E. Weinan, 2004 .

A Gauss-Seidel projection method for micromagnetics simulations

E Weinan, E. Weinan, Hong Kong, 2001 .

Convergence of spectral methods for Burgers' equation

E Weinan, 1992 .

Accurate numerical methods for micromagnetics simulations with general geometries

E Weinan, Zydrunas Gimbutas, Carlos J. García-Cervera, 2003 .

Homogenization of scalar conservation laws with oscillatory forcing terms

E Weinan, E. Weinan, 1992 .

A thermodynamic study of the two-dimensional pressure-driven channel flow

E Weinan, Jianchun Wang, E. Weinan, 2016 .

Statistical properties of shocks in Burgers turbulence

E Weinan, Marco Avellaneda, M. Avellaneda, 1995 .

Analysis of multiscale methods

E Weinan, E. Weinan, P. Ming, 2004 .

Multiscale simulations in simple metals: A density-functional-based methodology

E Weinan, Efthimios Kaxiras, Gang Lu, 2004, cond-mat/0404414.

Orbital minimization with localization

E Weinan, Weiguo Gao, 2008 .

Response to "Comment on 'Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates' †J. Chem. Phys. 123, 194107 "2005…‡"

E Weinan, Eric Vanden-Eijnden, Di Liu, 2007 .

Misfit elastic energy and a continuum model for epitaxial growth with elasticity on vicinal surfaces

Yang Xiang, E Weinan, E. Weinan, 2004 .

Convergence of Fourier methods for the Navier-Stokes equations

E Weinan, E. Weinan, 1993 .

Invariant measures for Burgers equation with stochastic forcing

E Weinan, K. M. Khanin, E. Weinan, 2000, math/0005306.

Energy landscape and thermally activated switching of submicron-sized ferromagnetic elements

E Weinan, Eric Vanden-Eijnden, Weiqing Ren, 2003 .

Self-induced stochastic resonance in excitable systems

E Weinan, Eric Vanden-Eijnden, Cyrill B. Muratov, 2005 .

Small‐scale structures in Boussinesq convection

E Weinan, Chi-Wang Shu, Chi-Wang Shu, 1998 .

Hierarchical method for elliptic problems using wavelet

E Weinan, Zhiqiang Cai, 1992 .

Dynamics of vortex liquids in Ginzburg-Landau theories with applications to superconductivity.

E Weinan, E. Weinan, Weinan E, 1994, Physical review. B, Condensed matter.

Effective dynamics for ferromagnetic thin films

E Weinan, Carlos J. García-Cervera, E. Weinan, 2001 .

Linear-scaling subspace-iteration algorithm with optimally localized nonorthogonal wave functions for Kohn-Sham density functional theory

E Weinan, Carlos J. García-Cervera, Jianfeng Lu, 2009 .

A Priori Estimates for Two-layer Neural Networks

E Weinan, Chao Ma, Lei Wu, 2018 .

Lattice Boltzmann Methods for Multiscale Fluid Problems

Sauro Succi, E Weinan, Efthimios Kaxiras, 2005 .

Minimum action method for the study of rare events

E Weinan, Eric Vanden-Eijnden, Weiqing Ren, 2004 .

Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids

E Weinan, Jian-Guo Liu, Jian‐Guo Liu, 1997 .

Probing Multi-Scale Energy Landscapes Using the String Method

E Weinan, Eric Vanden-Eijnden, Weiqing Ren, 2002 .

Model the nonlinear instability of wall-bounded shear flows as a rare event: a study on two-dimensional Poiseuille flow

E Weinan, Haijun Yu, Xiaoliang Wan, 2015 .

Analysis of the Local Quasicontinuum Method

E Weinan, Pingbing Ming, P. Ming, 2006 .

Pole-Based approximation of the Fermi-Dirac function

E Weinan, Lexing Ying, Jianfeng Lu, 2009, 0906.1319.

Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems

E Weinan, Jianfeng Lu, Roberto Car, 2008, 0812.4352.

Uniform Accuracy of the Quasicontinuum Method

E Weinan, Jianfeng Lu, Jerry Zhijian Yang, 2006, MRS Online Proceedings Library.

Brownian ratchets and the photoalignment of liquid crystals

E Weinan, Peter Palffy-Muhoray, E. Weinan, 2002 .

Multiscale modeling of the dynamics of solids at finite temperature

E Weinan, Xiantao Li, E. Weinan, 2005 .

Sequential multiscale modeling using sparse representation

E Weinan, Carlos J. García-Cervera, Weiqing Ren, 2008 .

Pushing the Limit of Molecular Dynamics with Ab Initio Accuracy to 100 Million Atoms with Machine Learning

E Weinan, Weile Jia, Lin Lin, 2020, SC20: International Conference for High Performance Computing, Networking, Storage and Analysis.

Level set simulations of dislocation-particle bypass mechanisms

Yang Xiang, E Weinan, Li-Tien Cheng, 2004 .

The gentlest ascent dynamics

E Weinan, W. E, E. Weinan, 2010, 1011.0042.

Essentially Compact Schemes for Unsteady Viscous Incompressible Flows

E Weinan, E. Weinan, Jianguo Liu, 1996 .

Energy landscapes and rare events

E Weinan, Eric Vanden-Eijnden, Weiqing Ren, 2002 .

GAUGE METHOD FOR VISCOUS INCOMPRESSIBLE FLOWS

E Weinan, E. Weinan, Jianguo Liu, 2003 .

Subcritical bifurcation in spatially extended systems

E Weinan, Xiuyuan Cheng, W. E, 2012 .

Optimized local basis function for Kohn-Sham density functional theory

E Weinan, Lexing Ying, Jianfeng Lu, 2011 .

Correctors for the homogenization of conservation laws with oscillatory forcing terms

E Weinan, Denis Serre, D. Serre, 1992 .

A dynamic atomistic-continuum method for the simulation of crystalline materials

E Weinan, Zhongyi Huang, E. Weinan, 2001 .

The Kohn-Sham Equation for Deformed Crystals

E Weinan, Jianfeng Lu, E. Weinan, 2012 .

BLOWUP OF SOLUTIONS OF THE UNSTEADY PRANDTL'S EQUATION

E Weinan, Björn Engquist, B. Engquist, 1997 .

Onsager's conjecture on the energy conservation for solutions of Euler's equation

E Weinan, Edriss S. Titi, Peter Constantin, 1994 .

Variational boundary conditions for molecular dynamics simulations of crystalline solids at finite temperature: Treatment of the thermal bath

E Weinan, Xiantao Li, E. Weinan, 2007 .

Gauge finite element method for incompressible flows

E Weinan, Jian-Guo Liu, Jian‐Guo Liu, 2000 .

Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics

E Weinan, E. Weinan, Y. Sinai, 1996 .

Domain decomposition interface preconditioners for fourth-order elliptic problems

E Weinan, Tony F. Chan, Jiachang Sun, 1991 .

Continuum models for the contact line problem

E Weinan, Weiqing Ren, Dan Hu, 2010 .

Effective Maxwell equations from time-dependent density functional theory

E Weinan, Jianfeng Lu, Xu Yang, 2010, 1010.4912.