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E, Weinan

  1. The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems
    2017/09/30 by E, Weinan, Yu, Bing · 98 citations
    #35Q68 #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
  2. Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations
    2018/11/05 by Qianxiao Li, Cheng Tai, Li, Qianxiao +3 · 12 citations
    Economics, Econometrics and Finance · Computer Science · Mathematics · #Stochastic processes and financial applications #Stochastic Gradient Optimization Techniques #Mathematical Biology Tumor Growth
  3. Bridging Traditional and Machine Learning-based Algorithms for Solving PDEs: The Random Feature Method
    2022/07/27 by Jingrun Chen, Xurong Chi, Chen, Jingrun +5 · 16 citations
    Computer Science · Environmental Science · #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Hydrological Forecasting Using AI #Image Processing and 3D Reconstruction #Neural Networks and Applications #Numerical Analysis (math.NA)
  4. Stochastic modified equations and adaptive stochastic gradient algorithms
    2015/11/19 by Li, Qianxiao, Tai, Cheng, E, Weinan · 9 citations
    #68W20 #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
  5. Deep Learning Approximation for Stochastic Control Problems
    2016/11/02 by Han, Jiequn, E, Weinan · 9 citations
    #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural and Evolutionary Computing (cs.NE) #Optimization and Control (math.OC)
  6. Towards Theoretically Understanding Why SGD Generalizes Better Than ADAM in Deep Learning
    2020/10/12 by Pan Zhou, Zhou, Pan, Jiashi Feng +9 · 11 citations
    Computer Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques
  7. Pushing the limit of molecular dynamics with ab initio accuracy to 100 million atoms with machine learning
    2020/05/01 by Jia, Weile, Wang, Han, Chen, Mohan +5 · 10 citations
    #Computational Physics (physics.comp-ph) #FOS: Physical sciences
  8. Convolutional neural networks with low-rank regularization
    2015/11/19 by Cheng Tai, Tai, Cheng, Tong Xiao +7 · 10 citations
    Computer Science · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Face and Expression Recognition #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications
  9. Understanding and Enhancing the Transferability of Adversarial Examples
    2018/02/27 by Lei Wu, Zhanxing Zhu, Wu, Lei +5 · 11 citations
    Computer Science · #Advanced Malware Detection Techniques #Adversarial Robustness in Machine Learning #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Security and Verification in Computing
  10. PaSa: An LLM Agent for Comprehensive Academic Paper Search
    2025/01/17 by Yichen He, Guanhua Huang, He, Yichen +13 · 1 voice · 22 citations
    Computer Science · #Data Mining Algorithms and Applications #Educational Technology and Assessment #FOS: Computer and information sciences #Information Retrieval (cs.IR) #Machine Learning (cs.LG) #Semantic Web and Ontologies #cs.IR #cs.LG
  11. Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't
    2020/09/22 by E, Weinan, Ma, Chao, Wojtowytsch, Stephan +1 · 7 citations
    #26B40 #35Q68 #41A30 #68T07 (primary) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA)
  12. Noisy Hegselmann-Krause Systems: Phase Transition and the 2R-Conjecture
    2015/11/10 by Wang, Chu, Li, Qianxiao, E, Weinan +1 · 5 citations
    #FOS: Mathematics #Optimization and Control (math.OC)
  13. Representation formulas and pointwise properties for Barron functions
    2020/06/10 by E, Weinan, Wojtowytsch, Stephan · 5 citations
    #26B35 #26B40 #46E15 #68T07 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Machine Learning (cs.LG) #Machine Learning (stat.ML)
  14. Some observations on high-dimensional partial differential equations with Barron data
    2020/12/02 by E, Weinan, Wojtowytsch, Stephan · 5 citations
    #35C15 #65M80 #68T07 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG)
  15. Can Shallow Neural Networks Beat the Curse of Dimensionality? A mean field training perspective
    2020/05/21 by Stephan Wojtowytsch, Wojtowytsch, Stephan, E Weinan +1 · 5 citations
    Computer Science · Physics and Astronomy · #49Q22 #68T07 #68W25 #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications #Stochastic Gradient Optimization Techniques
  16. Towards Understanding Generalization of Deep Learning: Perspective of Loss Landscapes
    2017/06/30 by Wu, Lei, Zhu, Zhanxing, E, Weinan · 3 citations
    #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
  17. Statistical Theory for the Stochastic Burgers Equation in the Inviscid Limit
    1999/04/15 by Weinan E, E, Weinan, Eric Vanden Eijnden +1 · 2 citations
    Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #chao-dyn #nlin.CD
  18. Monge-Ampère Flow for Generative Modeling
    2018/09/26 by Zhang, Linfeng, E, Weinan, Wang, Lei · 3 citations
    #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Mechanics (cond-mat.stat-mech)
  19. The Random Feature Method for Time-dependent Problems
    2023/04/14 by Jingrun Chen, E Weinan, Chen, Jingrun +3 · 5 citations
    Decision Sciences · Environmental Science · #65M20 #65M55 #65M70 #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Soil Geostatistics and Mapping
  20. The Barron Space and the Flow-induced Function Spaces for Neural Network Models
    2019/06/18 by E Weinan, E, Weinan, Chao Ma +3 · 3 citations
    Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Model Reduction and Neural Networks #Neural Networks and Applications #Probability (math.PR)
  21. A Qualitative Study of the Dynamic Behavior for Adaptive Gradient Algorithms
    2020/09/14 by Ma, Chao, Wu, Lei, E, Weinan · 3 citations
    #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
  22. Uni-Mol2: Exploring Molecular Pretraining Model at Scale
    2024/06/21 by Xiaohong Ji, Zhen Wang, Ji, Xiaohong +11 · 7 citations
    Chemistry · #Various Chemistry Research Topics
  23. Understanding the Expressive Power and Mechanisms of Transformer for Sequence Modeling
    2024/02/01 by Wang, Mingze, E, Weinan · 5 citations
    #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
  24. SciMaster: Towards General-Purpose Scientific AI Agents, Part I. X-Master as Foundation: Can We Lead on Humanity's Last Exam?
    2025/07/07 by Chai, Jingyi, Shuo Tang, Tang, Shuo +18 · 19 citations
    Computer Science · Medicine · #Artificial Intelligence (cs.AI) #Artificial Intelligence in Healthcare and Education #Computation and Language (cs.CL) #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #Topic Modeling
  25. Functional Frank-Wolfe Boosting for General Loss Functions
    2015/10/09 by Chu Wang, Wang, Chu, Yingfei Wang +5 · 2 citations
    Computer Science · Engineering · #Machine Learning and Algorithms #Sparse and Compressive Sensing Techniques #Face and Expression Recognition
  26. Exponential Convergence of the Deep Neural Network Approximation for Analytic Functions
    2018/07/01 by E Weinan, Qingcan Wang, E, Weinan +1 · 2 citations
    Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Neural Networks and Applications
  27. ML-Master: Towards AI-for-AI via Integration of Exploration and Reasoning
    2025/06/19 by Liu, Zexi, Cai, Yuzhu, Zhu, Xinyu +6 · 13 citations
    #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG)
  28. A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics
    2022/01/09 by Zhang, Tianhan, Yi, Yuxiao, Xu, Yifan +4 · 3 citations
    #Chemical Physics (physics.chem-ph) #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Machine Learning (cs.LG) #Numerical Analysis (math.NA)
  29. On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers
    2020/12/10 by E Weinan, E, Weinan, Stephan Wojtowytsch +1 · 2 citations
    Computer Science · #Neural Networks and Applications
  30. On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis
    2020/09/16 by Zhong Li, Li, Zhong, Jiequn Han +5 · 3 citations
    Computer Science · Neuroscience · Physics and Astronomy · #37M10 #68T07 #68W25 #FOS: Computer and information sciences #FOS: Mathematics #I.2.6 #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications #Neural dynamics and brain function #Optimization and Control (math.OC)
  31. Energy landscapes and rare events
    2002/12/01 by E, Weinan, Ren, Weiqing, Vanden-Eijnden, Eric · 1 citation
    #60-08 #60F10 #65C #FOS: Mathematics #Numerical Analysis (math.NA)
  32. A Machine Learning Enhanced Algorithm for the Optimal Landing Problem
    2022/03/13 by Yaohua Zang, Zang, Yaohua, Jihao Long +9 · 2 citations
    Engineering · #Aerospace and Aviation Technology #FOS: Mathematics #Optimization and Control (math.OC) #Real-time simulation and control systems #Vehicle Dynamics and Control Systems
  33. Effective Maxwell equations from time-dependent density functional theory
    2010/10/23 by E, Weinan, Lu, Jianfeng, Yang, Xu · 1 citation
    #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mathematical Physics (math-ph)
  34. The Sharpness Disparity Principle in Transformers for Accelerating Language Model Pre-Training
    2025/02/26 by Jinbo Wang, Wang, Jinbo, Wang, Mingze +8 · 5 citations
    Computer Science · Medicine · #Topic Modeling #Artificial Intelligence in Healthcare and Education #Domain Adaptation and Few-Shot Learning
  35. Anchor function: a type of benchmark functions for studying language models
    2024/01/16 by Zhang, Zhongwang, Wang, Zhiwei, Yao, Junjie +4 · 3 citations
    #Computation and Language (cs.CL) #FOS: Computer and information sciences #Machine Learning (cs.LG)
  36. Model Reduction with Memory and the Machine Learning of Dynamical Systems
    2018/08/10 by Ma, Chao, Wang, Jianchun, E, Weinan · 1 citation
    #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
  37. Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels
    2020/05/21 by E Weinan, Stephan Wojtowytsch, E, Weinan +1 · 3 citations
    Computer Science · Engineering · #Neural Networks and Applications #Stochastic Gradient Optimization Techniques #Sparse and Compressive Sensing Techniques
  38. Improving Generalization and Convergence by Enhancing Implicit Regularization
    2024/05/31 by Wang, Mingze, Wang, Jinbo, He, Haotian +6 · 2 citations
    #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC)
  39. LAMBench: A Benchmark for Large Atomistic Models
    2025/04/28 by Anyang Peng, Chun Cai, Peng, Anyang +21 · 4 citations
    Materials Science · #Machine Learning in Materials Science
  40. DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks
    2021/12/29 by Han, Jiequn, Yang, Yucheng, E, Weinan · 1 citation
    #FOS: Computer and information sciences #FOS: Economics and business #General Economics (econ.GN) #Machine Learning (cs.LG)
  41. Intelligent System for Automated Molecular Patent Infringement Assessment
    2024/12/10 by Sihang Li, Shi, Yaorui, Li, Sihang +26 · 2 citations
    Computer Science · #Computational Drug Discovery Methods
  42. Strategic priorities for transformative progress in advancing biology with proteomics and artificial intelligence
    2025/02/21 by Yingying Sun, Jun A, Sun, Yingying +121 · 3 voices · 1 citation
    #q-bio.OT #cs.AI
  43. NMR-Solver: Automated Structure Elucidation via Large-Scale Spectral Matching and Physics-Guided Fragment Optimization
    2025/08/30 by Jin, Yongqi, Wang, Jun-Jie, Xu, Fanjie +6 · 3 citations
    #Artificial Intelligence (cs.AI) #Chemical Physics (physics.chem-ph) #FOS: Computer and information sciences #FOS: Physical sciences
  44. Uni-ELF: A Multi-Level Representation Learning Framework for Electrolyte Formulation Design
    2024/07/08 by Boshen Zeng, S. J. Chen, Zeng, Boshen +17 · 1 citation
    Engineering · #Artificial Intelligence (cs.AI) #Chemical Physics (physics.chem-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Process Optimization and Integration
  45. Unified Cross-Scale 3D Generation and Understanding via Autoregressive Modeling
    2025/03/20 by S.C. Lu, Haowei Lin, Lu, Shuqi +15 · 2 citations
    Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · #Biomolecules (q-bio.BM) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Physical sciences #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning in Materials Science #Materials Science (cond-mat.mtrl-sci) #Protein Structure and Dynamics
  46. How Transformers Get Rich: Approximation and Dynamics Analysis
    2024/10/15 by Wang, Mingze, Raymond C. Yu, E Weinan +4 · 1 citation
    Engineering · #Electric Motor Design and Analysis #Oil and Gas Production Techniques #Electric Power Systems and Control
  47. A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
    2025/05/07 by Han, Jiequn, Jentzen, Arnulf, E, Weinan · 2 citations
    #Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #and Science (cs.CE)
  48. Discovery of High-Temperature Superconducting Ternary Hydrides via Deep Learning
    2025/02/23 by Xiaoyang Wang, Wang, Xiaoyang, Chengqian Zhang +13 · 1 citation
    Engineering · Computer Science · #Superconducting Materials and Applications #Topic Modeling
  49. Solving multiscale dynamical systems by deep learning
    2024/01/02 by Junjie Yao, Yao, Junjie, Yuxiao Yi +12 · 1 citation
    Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Model Reduction and Neural Networks #Numerical Analysis (math.NA)
  50. Ab Initio bulk free energy surface of proper ferroelectrics
    2022/05/24 by Xie, Pinchen, Chen, Yixiao, Xu, Xinyu +3 · 1 citation
    #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci)
  51. Inverse Knowledge Search over Verifiable Reasoning: Synthesizing a Scientific Encyclopedia from a Long Chains-of-Thought Knowledge Base
    2025/10/30 by Yu Li, Li, Yu, Yuan Huang +46 · 2 voices · 1 citation
    Computer Science · Decision Sciences · Materials Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning in Materials Science #Mathematics, Computing, and Information Processing #Scientific Computing and Data Management #cs.AI #cs.LG