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


Jan 09, 2022
Tianhan Zhang, Yuxiao Yi, Yifan Xu, Zhi X. Chen, Yaoyu Zhang, Weinan E, Zhi-Qin John Xu


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


Jan 07, 2022
Zhiwei Wang, Yaoyu Zhang, Yiguang Ju, Weinan E, Zhi-Qin John Xu, Tianhan Zhang


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DeePN$^2$: A deep learning-based non-Newtonian hydrodynamic model


Dec 29, 2021
Lidong Fang, Pei Ge, Lei Zhang, Huan Lei, Weinan E


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


Dec 29, 2021
Jiequn Han, Yucheng Yang, Weinan E


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Generalization Error of GAN from the Discriminator's Perspective


Jul 08, 2021
Hongkang Yang, Weinan E


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An $L^2$ Analysis of Reinforcement Learning in High Dimensions with Kernel and Neural Network Approximation


Apr 19, 2021
Jihao Long, Jiequn Han, Weinan E


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Generalization and Memorization: The Bias Potential Model


Jan 06, 2021
Hongkang Yang, Weinan E

* Improved error estimate 

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


Dec 19, 2020
Weinan E, Stephan Wojtowytsch


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


Dec 10, 2020
Weinan E, Stephan Wojtowytsch


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A deep learning-based ODE solver for chemical kinetics


Nov 24, 2020
Tianhan Zhang, Yaoyu Zhang, Weinan E, Yiguang Ju


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Interpretable Neural Networks for Panel Data Analysis in Economics


Oct 27, 2020
Yucheng Yang, Zhong Zheng, Weinan E


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


Oct 12, 2020
Pan Zhou, Jiashi Feng, Chao Ma, Caiming Xiong, Steven HOI, Weinan E

* NeurIPS 2020 

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The Knowledge Graph for Macroeconomic Analysis with Alternative Big Data


Oct 11, 2020
Yucheng Yang, Yue Pang, Guanhua Huang, Weinan E


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


Oct 04, 2020
Haijun Yu, Xinyuan Tian, Weinan E, Qianxiao Li

* 37 pages, 17 figures 

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Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't


Oct 01, 2020
Weinan E, Chao Ma, Stephan Wojtowytsch, Lei Wu

* Review article. Feedback welcome 

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A priori estimates for classification problems using neural networks


Sep 28, 2020
Weinan E, Stephan Wojtowytsch


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Machine Learning and Computational Mathematics


Sep 23, 2020
Weinan E


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


Sep 16, 2020
Zhong Li, Jiequn Han, Weinan E, Qianxiao Li


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A Qualitative Study of the Dynamic Behavior of Adaptive Gradient Algorithms


Sep 14, 2020
Chao Ma, Lei Wu, Weinan E


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


Aug 13, 2020
Chao Ma, Lei Wu, Weinan E


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DeePKS: a comprehensive data-driven approach towards chemically accurate density functional theory


Aug 01, 2020
Yixiao Chen, Linfeng Zhang, Han Wang, Weinan E


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On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics


Jul 30, 2020
Weinan E, Stephan Wojtowytsch


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Coarse-grained spectral projection (CGSP): A scalable and parallelizable deep learning-based approach to quantum unitary dynamics


Jul 19, 2020
Pinchen Xie, Weinan E


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


Jun 25, 2020
Chao Ma, Lei Wu, Weinan E

* 23 pages 

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Representation formulas and pointwise properties for Barron functions


Jun 10, 2020
Weinan E, Stephan Wojtowytsch


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