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ORCIDBibTeX records: Weinan E
@article{DBLP:journals/corr/abs-2401-01220,
author = {Zhi{-}Qin John Xu and
Junjie Yao and
Yuxiao Yi and
Liangkai Hang and
Weinan E and
Yaoyu Zhang and
Tianhan Zhang},
title = {Solving multiscale dynamical systems by deep learning},
journal = {CoRR},
volume = {abs/2401.01220},
year = {2024},
url = {https://doi.org/10.48550/arXiv.2401.01220},
doi = {10.48550/ARXIV.2401.01220},
eprinttype = {arXiv},
eprint = {2401.01220},
timestamp = {Mon, 15 Jan 2024 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2401-01220.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2401-08309,
author = {Zhongwang Zhang and
Zhiwei Wang and
Junjie Yao and
Zhangchen Zhou and
Xiaolong Li and
Weinan E and
Zhi{-}Qin John Xu},
title = {Anchor function: a type of benchmark functions for studying language
models},
journal = {CoRR},
volume = {abs/2401.08309},
year = {2024},
url = {https://doi.org/10.48550/arXiv.2401.08309},
doi = {10.48550/ARXIV.2401.08309},
eprinttype = {arXiv},
eprint = {2401.08309},
timestamp = {Thu, 01 Feb 2024 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2401-08309.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2402-00522,
author = {Mingze Wang and
Weinan E},
title = {Understanding the Expressive Power and Mechanisms of Transformer for
Sequence Modeling},
journal = {CoRR},
volume = {abs/2402.00522},
year = {2024},
url = {https://doi.org/10.48550/arXiv.2402.00522},
doi = {10.48550/ARXIV.2402.00522},
eprinttype = {arXiv},
eprint = {2402.00522},
timestamp = {Fri, 09 Feb 2024 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2402-00522.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@book{DBLP:books/ws/OuZDELS23,
author = {Gaoyan Ou and
Zhanxing Zhu and
Bin Dong and
Weinan E and
Binyang Li and
Shumin Shi},
title = {Introduction to Data Science},
publisher = {WorldScientific},
year = {2023},
url = {https://doi.org/10.1142/13071},
doi = {10.1142/13071},
isbn = {9789811263897},
timestamp = {Wed, 20 Mar 2024 00:00:00 +0100},
biburl = {https://dblp.org/rec/books/ws/OuZDELS23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/cphysics/ChenZWE23,
author = {Yixiao Chen and
Linfeng Zhang and
Han Wang and
Weinan E},
title = {DeePKS-kit: {A} package for developing machine learning-based chemically
accurate energy and density functional models},
journal = {Comput. Phys. Commun.},
volume = {282},
pages = {108520},
year = {2023},
url = {https://doi.org/10.1016/j.cpc.2022.108520},
doi = {10.1016/J.CPC.2022.108520},
timestamp = {Mon, 28 Aug 2023 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/cphysics/ChenZWE23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/emnlp/HuangXZCYE23,
author = {Guanhua Huang and
Runxin Xu and
Ying Zeng and
Jiaze Chen and
Zhouwang Yang and
Weinan E},
editor = {Houda Bouamor and
Juan Pino and
Kalika Bali},
title = {An Iteratively Parallel Generation Method with the Pre-Filling Strategy
for Document-level Event Extraction},
booktitle = {Proceedings of the 2023 Conference on Empirical Methods in Natural
Language Processing, {EMNLP} 2023, Singapore, December 6-10, 2023},
pages = {10834--10852},
publisher = {Association for Computational Linguistics},
year = {2023},
url = {https://doi.org/10.18653/v1/2023.emnlp-main.668},
doi = {10.18653/V1/2023.EMNLP-MAIN.668},
timestamp = {Fri, 12 Apr 2024 01:00:00 +0200},
biburl = {https://dblp.org/rec/conf/emnlp/HuangXZCYE23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2302-03498,
author = {Zeping Min and
Qian Ge and
Zhong Li and
Weinan E},
title = {{AMP:} {A} unified framework boosting low resource automatic speech
recognition},
journal = {CoRR},
volume = {abs/2302.03498},
year = {2023},
url = {https://doi.org/10.48550/arXiv.2302.03498},
doi = {10.48550/ARXIV.2302.03498},
eprinttype = {arXiv},
eprint = {2302.03498},
timestamp = {Sun, 19 Feb 2023 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2302-03498.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2304-06913,
author = {Jingrun Chen and
Weinan E and
Yixin Luo},
title = {The Random Feature Method for Time-dependent Problems},
journal = {CoRR},
volume = {abs/2304.06913},
year = {2023},
url = {https://doi.org/10.48550/arXiv.2304.06913},
doi = {10.48550/ARXIV.2304.06913},
eprinttype = {arXiv},
eprint = {2304.06913},
timestamp = {Wed, 19 Apr 2023 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2304-06913.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2305-01243,
author = {Jun Zhang and
Xiaohan Lin and
Weinan E and
Yi Qin Gao},
title = {Machine-Learned Invertible Coarse Graining for Multiscale Molecular
Modeling},
journal = {CoRR},
volume = {abs/2305.01243},
year = {2023},
url = {https://doi.org/10.48550/arXiv.2305.01243},
doi = {10.48550/ARXIV.2305.01243},
eprinttype = {arXiv},
eprint = {2305.01243},
timestamp = {Fri, 05 May 2023 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2305-01243.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2311-17749,
author = {Wei Hu and
Yue Zhao and
Weinan E and
Jiequn Han and
Jihao Long},
title = {Learning Free Terminal Time Optimal Closed-loop Control of Manipulators},
journal = {CoRR},
volume = {abs/2311.17749},
year = {2023},
url = {https://doi.org/10.48550/arXiv.2311.17749},
doi = {10.48550/ARXIV.2311.17749},
eprinttype = {arXiv},
eprint = {2311.17749},
timestamp = {Tue, 05 Dec 2023 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2311-17749.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jmlr/LiHEL22,
author = {Zhong Li and
Jiequn Han and
Weinan E and
Qianxiao Li},
title = {Approximation and Optimization Theory for Linear Continuous-Time Recurrent
Neural Networks},
journal = {J. Mach. Learn. Res.},
volume = {23},
pages = {42:1--42:85},
year = {2022},
url = {http://jmlr.org/papers/v23/21-0368.html},
timestamp = {Wed, 16 Feb 2022 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/jmlr/LiHEL22.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/ncs/WangWCZWE22,
author = {Dongdong Wang and
Yanze Wang and
Junhan Chang and
Linfeng Zhang and
Han Wang and
Weinan E},
title = {Efficient sampling of high-dimensional free energy landscapes using
adaptive reinforced dynamics},
journal = {Nat. Comput. Sci.},
volume = {2},
number = {1},
pages = {20--29},
year = {2022},
url = {https://doi.org/10.1038/s43588-021-00173-1},
doi = {10.1038/S43588-021-00173-1},
timestamp = {Mon, 15 Apr 2024 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/ncs/WangWCZWE22.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/pami/EZ22,
author = {Weinan E and
Yajun Zhou},
title = {A Mathematical Model for Universal Semantics},
journal = {{IEEE} Trans. Pattern Anal. Mach. Intell.},
volume = {44},
number = {3},
pages = {1124--1132},
year = {2022},
url = {https://doi.org/10.1109/TPAMI.2020.3022533},
doi = {10.1109/TPAMI.2020.3022533},
timestamp = {Wed, 16 Mar 2022 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/pami/EZ22.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/msml/ZangLZHEH22,
author = {Yaohua Zang and
Jihao Long and
Xuanxi Zhang and
Wei Hu and
Weinan E and
Jiequn Han},
editor = {Bin Dong and
Qianxiao Li and
Lei Wang and
Zhi{-}Qin John Xu},
title = {A Machine Learning Enhanced Algorithm for the Optimal Landing Problem},
booktitle = {Mathematical and Scientific Machine Learning, 15-17 August 2022, Peking
University, Beijing, China},
series = {Proceedings of Machine Learning Research},
volume = {190},
pages = {319--334},
publisher = {{PMLR}},
year = {2022},
url = {https://proceedings.mlr.press/v190/zang22a.html},
timestamp = {Wed, 09 Aug 2023 17:07:50 +0200},
biburl = {https://dblp.org/rec/conf/msml/ZangLZHEH22.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2201-02025,
author = {Zhiwei Wang and
Yaoyu Zhang and
Yiguang Ju and
Weinan E and
Zhi{-}Qin John Xu and
Tianhan Zhang},
title = {A deep learning-based model reduction (DeePMR) method for simplifying
chemical kinetics},
journal = {CoRR},
volume = {abs/2201.02025},
year = {2022},
url = {https://arxiv.org/abs/2201.02025},
eprinttype = {arXiv},
eprint = {2201.02025},
timestamp = {Mon, 10 Jan 2022 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2201-02025.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2201-03549,
author = {Tianhan Zhang and
Yuxiao Yi and
Yifan Xu and
Zhi X. Chen and
Yaoyu Zhang and
Weinan E and
Zhi{-}Qin John Xu},
title = {A multi-scale sampling method for accurate and robust deep neural
network to predict combustion chemical kinetics},
journal = {CoRR},
volume = {abs/2201.03549},
year = {2022},
url = {https://arxiv.org/abs/2201.03549},
eprinttype = {arXiv},
eprint = {2201.03549},
timestamp = {Fri, 21 Jan 2022 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2201-03549.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2207-13380,
author = {Jingrun Chen and
Xurong Chi and
Weinan E and
Zhouwang Yang},
title = {Bridging Traditional and Machine Learning-based Algorithms for Solving
PDEs: The Random Feature Method},
journal = {CoRR},
volume = {abs/2207.13380},
year = {2022},
url = {https://doi.org/10.48550/arXiv.2207.13380},
doi = {10.48550/ARXIV.2207.13380},
eprinttype = {arXiv},
eprint = {2207.13380},
timestamp = {Mon, 01 Aug 2022 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2207-13380.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/cphysics/LuWCLCEJZ21,
author = {Denghui Lu and
Han Wang and
Mohan Chen and
Lin Lin and
Roberto Car and
Weinan E and
Weile Jia and
Linfeng Zhang},
title = {86 {PFLOPS} Deep Potential Molecular Dynamics simulation of 100 million
atoms with \emph{ab initio} accuracy},
journal = {Comput. Phys. Commun.},
volume = {259},
pages = {107624},
year = {2021},
url = {https://doi.org/10.1016/j.cpc.2020.107624},
doi = {10.1016/J.CPC.2020.107624},
timestamp = {Mon, 28 Aug 2023 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/cphysics/LuWCLCEJZ21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/iclr/LiHEL21,
author = {Zhong Li and
Jiequn Han and
Weinan E and
Qianxiao Li},
title = {On the Curse of Memory in Recurrent Neural Networks: Approximation
and Optimization Analysis},
booktitle = {9th International Conference on Learning Representations, {ICLR} 2021,
Virtual Event, Austria, May 3-7, 2021},
publisher = {OpenReview.net},
year = {2021},
url = {https://openreview.net/forum?id=8Sqhl-nF50},
timestamp = {Wed, 23 Jun 2021 17:36:39 +0200},
biburl = {https://dblp.org/rec/conf/iclr/LiHEL21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/msml/EW21,
author = {Weinan E and
Stephan Wojtowytsch},
editor = {Joan Bruna and
Jan S. Hesthaven and
Lenka Zdeborov{\'{a}}},
title = {Some observations on high-dimensional partial differential equations
with Barron data},
booktitle = {Mathematical and Scientific Machine Learning, 16-19 August 2021, Virtual
Conference / Lausanne, Switzerland},
series = {Proceedings of Machine Learning Research},
volume = {145},
pages = {253--269},
publisher = {{PMLR}},
year = {2021},
url = {https://proceedings.mlr.press/v145/e22a.html},
timestamp = {Fri, 20 May 2022 12:50:15 +0200},
biburl = {https://dblp.org/rec/conf/msml/EW21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/msml/EW21a,
author = {Weinan E and
Stephan Wojtowytsch},
editor = {Joan Bruna and
Jan S. Hesthaven and
Lenka Zdeborov{\'{a}}},
title = {On the emergence of simplex symmetry in the final and penultimate
layers of neural network classifiers},
booktitle = {Mathematical and Scientific Machine Learning, 16-19 August 2021, Virtual
Conference / Lausanne, Switzerland},
series = {Proceedings of Machine Learning Research},
volume = {145},
pages = {270--290},
publisher = {{PMLR}},
year = {2021},
url = {https://proceedings.mlr.press/v145/e22b.html},
timestamp = {Fri, 20 May 2022 01:00:00 +0200},
biburl = {https://dblp.org/rec/conf/msml/EW21a.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/msml/0012WE21,
author = {Chao Ma and
Lei Wu and
Weinan E},
editor = {Joan Bruna and
Jan S. Hesthaven and
Lenka Zdeborov{\'{a}}},
title = {A Qualitative Study of the Dynamic Behavior for Adaptive Gradient
Algorithms},
booktitle = {Mathematical and Scientific Machine Learning, 16-19 August 2021, Virtual
Conference / Lausanne, Switzerland},
series = {Proceedings of Machine Learning Research},
volume = {145},
pages = {671--692},
publisher = {{PMLR}},
year = {2021},
url = {https://proceedings.mlr.press/v145/ma22a.html},
timestamp = {Fri, 20 May 2022 01:00:00 +0200},
biburl = {https://dblp.org/rec/conf/msml/0012WE21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/msml/YangE21,
author = {Hongkang Yang and
Weinan E},
editor = {Joan Bruna and
Jan S. Hesthaven and
Lenka Zdeborov{\'{a}}},
title = {Generalization and Memorization: The Bias Potential Model},
booktitle = {Mathematical and Scientific Machine Learning, 16-19 August 2021, Virtual
Conference / Lausanne, Switzerland},
series = {Proceedings of Machine Learning Research},
volume = {145},
pages = {1013--1043},
publisher = {{PMLR}},
year = {2021},
url = {https://proceedings.mlr.press/v145/yang22a.html},
timestamp = {Fri, 20 May 2022 01:00:00 +0200},
biburl = {https://dblp.org/rec/conf/msml/YangE21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2104-07794,
author = {Jihao Long and
Jiequn Han and
Weinan E},
title = {An L\({}^{\mbox{2}}\) Analysis of Reinforcement Learning in High Dimensions
with Kernel and Neural Network Approximation},
journal = {CoRR},
volume = {abs/2104.07794},
year = {2021},
url = {https://arxiv.org/abs/2104.07794},
eprinttype = {arXiv},
eprint = {2104.07794},
timestamp = {Mon, 19 Apr 2021 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2104-07794.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2107-03633,
author = {Hongkang Yang and
Weinan E},
title = {Generalization Error of {GAN} from the Discriminator's Perspective},
journal = {CoRR},
volume = {abs/2107.03633},
year = {2021},
url = {https://arxiv.org/abs/2107.03633},
eprinttype = {arXiv},
eprint = {2107.03633},
timestamp = {Tue, 20 Jul 2021 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2107-03633.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2112-14377,
author = {Jiequn Han and
Yucheng Yang and
Weinan E},
title = {DeepHAM: {A} Global Solution Method for Heterogeneous Agent Models
with Aggregate Shocks},
journal = {CoRR},
volume = {abs/2112.14377},
year = {2021},
url = {https://arxiv.org/abs/2112.14377},
eprinttype = {arXiv},
eprint = {2112.14377},
timestamp = {Wed, 05 Jan 2022 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2112-14377.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2112-14798,
author = {Lidong Fang and
Pei Ge and
Lei Zhang and
Huan Lei and
Weinan E},
title = {DeePN\({}^{\mbox{2}}\): {A} deep learning-based non-Newtonian hydrodynamic
model},
journal = {CoRR},
volume = {abs/2112.14798},
year = {2021},
url = {https://arxiv.org/abs/2112.14798},
eprinttype = {arXiv},
eprint = {2112.14798},
timestamp = {Wed, 05 Jan 2022 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2112-14798.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/cphysics/ZhangWCZZWE20,
author = {Yuzhi Zhang and
Haidi Wang and
Weijie Chen and
Jinzhe Zeng and
Linfeng Zhang and
Han Wang and
Weinan E},
title = {{DP-GEN:} {A} concurrent learning platform for the generation of reliable
deep learning based potential energy models},
journal = {Comput. Phys. Commun.},
volume = {253},
pages = {107206},
year = {2020},
url = {https://doi.org/10.1016/j.cpc.2020.107206},
doi = {10.1016/J.CPC.2020.107206},
timestamp = {Wed, 04 Aug 2021 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/cphysics/ZhangWCZZWE20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/tai/WojtowytschE20,
author = {Stephan Wojtowytsch and
Weinan E},
title = {Can Shallow Neural Networks Beat the Curse of Dimensionality? {A}
Mean Field Training Perspective},
journal = {{IEEE} Trans. Artif. Intell.},
volume = {1},
number = {2},
pages = {121--129},
year = {2020},
url = {https://doi.org/10.1109/TAI.2021.3051357},
doi = {10.1109/TAI.2021.3051357},
timestamp = {Thu, 16 Sep 2021 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/tai/WojtowytschE20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icassp/DonEM20,
author = {Zehao Don and
Weinan E and
Chao Ma},
title = {A Priori Estimates of the Generalization Error for Autoencoders},
booktitle = {2020 {IEEE} International Conference on Acoustics, Speech and Signal
Processing, {ICASSP} 2020, Barcelona, Spain, May 4-8, 2020},
pages = {3327--3331},
publisher = {{IEEE}},
year = {2020},
url = {https://doi.org/10.1109/ICASSP40776.2020.9053874},
doi = {10.1109/ICASSP40776.2020.9053874},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/conf/icassp/DonEM20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/msml/MaWE20,
author = {Chao Ma and
Lei Wu and
Weinan E},
editor = {Jianfeng Lu and
Rachel A. Ward},
title = {The Slow Deterioration of the Generalization Error of the Random Feature
Model},
booktitle = {Proceedings of Mathematical and Scientific Machine Learning, {MSML}
2020, 20-24 July 2020, Virtual Conference / Princeton, NJ, {USA}},
series = {Proceedings of Machine Learning Research},
volume = {107},
pages = {373--389},
publisher = {{PMLR}},
year = {2020},
url = {http://proceedings.mlr.press/v107/ma20a.html},
timestamp = {Thu, 04 Jan 2024 08:18:06 +0100},
biburl = {https://dblp.org/rec/conf/msml/MaWE20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/nips/ZhouF0XHE20,
author = {Pan Zhou and
Jiashi Feng and
Chao Ma and
Caiming Xiong and
Steven Chu{-}Hong Hoi and
Weinan E},
editor = {Hugo Larochelle and
Marc'Aurelio Ranzato and
Raia Hadsell and
Maria{-}Florina Balcan and
Hsuan{-}Tien Lin},
title = {Towards Theoretically Understanding Why Sgd Generalizes Better Than
Adam in Deep Learning},
booktitle = {Advances in Neural Information Processing Systems 33: Annual Conference
on Neural Information Processing Systems 2020, NeurIPS 2020, December
6-12, 2020, virtual},
year = {2020},
url = {https://proceedings.neurips.cc/paper/2020/hash/f3f27a324736617f20abbf2ffd806f6d-Abstract.html},
timestamp = {Tue, 19 Jan 2021 00:00:00 +0100},
biburl = {https://dblp.org/rec/conf/nips/ZhouF0XHE20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/sc/JiaWCL0CEZ20,
author = {Weile Jia and
Han Wang and
Mohan Chen and
Denghui Lu and
Lin Lin and
Roberto Car and
Weinan E and
Linfeng Zhang},
editor = {Christine Cuicchi and
Irene Qualters and
William T. Kramer},
title = {Pushing the limit of molecular dynamics with \emph{ab initio} accuracy
to 100 million atoms with machine learning},
booktitle = {Proceedings of the International Conference for High Performance Computing,
Networking, Storage and Analysis, {SC} 2020, Virtual Event / Atlanta,
Georgia, USA, November 9-19, 2020},
pages = {5},
publisher = {{IEEE/ACM}},
year = {2020},
url = {https://doi.org/10.1109/SC41405.2020.00009},
doi = {10.1109/SC41405.2020.00009},
timestamp = {Mon, 28 Aug 2023 01:00:00 +0200},
biburl = {https://dblp.org/rec/conf/sc/JiaWCL0CEZ20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2003-03672,
author = {Huan Lei and
Lei Wu and
Weinan E},
title = {Machine learning based non-Newtonian fluid model with molecular fidelity},
journal = {CoRR},
volume = {abs/2003.03672},
year = {2020},
url = {https://arxiv.org/abs/2003.03672},
eprinttype = {arXiv},
eprint = {2003.03672},
timestamp = {Tue, 10 Mar 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2003-03672.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2004-11658,
author = {Denghui Lu and
Han Wang and
Mohan Chen and
Jiduan Liu and
Lin Lin and
Roberto Car and
Weinan E and
Weile Jia and
Linfeng Zhang},
title = {86 {PFLOPS} Deep Potential Molecular Dynamics simulation of 100 million
atoms with ab initio accuracy},
journal = {CoRR},
volume = {abs/2004.11658},
year = {2020},
url = {https://arxiv.org/abs/2004.11658},
eprinttype = {arXiv},
eprint = {2004.11658},
timestamp = {Mon, 22 Jun 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2004-11658.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2005-10807,
author = {Weinan E and
Stephan Wojtowytsch},
title = {Kolmogorov Width Decay and Poor Approximators in Machine Learning:
Shallow Neural Networks, Random Feature Models and Neural Tangent
Kernels},
journal = {CoRR},
volume = {abs/2005.10807},
year = {2020},
url = {https://arxiv.org/abs/2005.10807},
eprinttype = {arXiv},
eprint = {2005.10807},
timestamp = {Sat, 23 Jan 2021 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2005-10807.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2005-10815,
author = {Stephan Wojtowytsch and
Weinan E},
title = {Can Shallow Neural Networks Beat the Curse of Dimensionality? {A}
mean field training perspective},
journal = {CoRR},
volume = {abs/2005.10815},
year = {2020},
url = {https://arxiv.org/abs/2005.10815},
eprinttype = {arXiv},
eprint = {2005.10815},
timestamp = {Fri, 22 May 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2005-10815.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2006-02619,
author = {Weinan E and
Jiequn Han and
Linfeng Zhang},
title = {Integrating Machine Learning with Physics-Based Modeling},
journal = {CoRR},
volume = {abs/2006.02619},
year = {2020},
url = {https://arxiv.org/abs/2006.02619},
eprinttype = {arXiv},
eprint = {2006.02619},
timestamp = {Tue, 09 Jun 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2006-02619.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2006-05982,
author = {Weinan E and
Stephan Wojtowytsch},
title = {Representation formulas and pointwise properties for Barron functions},
journal = {CoRR},
volume = {abs/2006.05982},
year = {2020},
url = {https://arxiv.org/abs/2006.05982},
eprinttype = {arXiv},
eprint = {2006.05982},
timestamp = {Fri, 12 Jun 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2006-05982.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2006-14450,
author = {Chao Ma and
Lei Wu and
Weinan E},
title = {The Quenching-Activation Behavior of the Gradient Descent Dynamics
for Two-layer Neural Network Models},
journal = {CoRR},
volume = {abs/2006.14450},
year = {2020},
url = {https://arxiv.org/abs/2006.14450},
eprinttype = {arXiv},
eprint = {2006.14450},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2006-14450.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2007-09788,
author = {Pinchen Xie and
Weinan E},
title = {Coarse-grained spectral projection {(CGSP):} {A} scalable and parallelizable
deep learning-based approach to quantum unitary dynamics},
journal = {CoRR},
volume = {abs/2007.09788},
year = {2020},
url = {https://arxiv.org/abs/2007.09788},
eprinttype = {arXiv},
eprint = {2007.09788},
timestamp = {Wed, 29 Jul 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2007-09788.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2007-15623,
author = {Weinan E and
Stephan Wojtowytsch},
title = {On the Banach spaces associated with multi-layer ReLU networks: Function
representation, approximation theory and gradient descent dynamics},
journal = {CoRR},
volume = {abs/2007.15623},
year = {2020},
url = {https://arxiv.org/abs/2007.15623},
eprinttype = {arXiv},
eprint = {2007.15623},
timestamp = {Mon, 03 Aug 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2007-15623.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2008-00167,
author = {Yixiao Chen and
Linfeng Zhang and
Han Wang and
Weinan E},
title = {DeePKS: a comprehensive data-driven approach towards chemically accurate
density functional theory},
journal = {CoRR},
volume = {abs/2008.00167},
year = {2020},
url = {https://arxiv.org/abs/2008.00167},
eprinttype = {arXiv},
eprint = {2008.00167},
timestamp = {Sun, 09 Aug 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2008-00167.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2008-05621,
author = {Chao Ma and
Lei Wu and
Weinan E},
title = {The Slow Deterioration of the Generalization Error of the Random Feature
Model},
journal = {CoRR},
volume = {abs/2008.05621},
year = {2020},
url = {https://arxiv.org/abs/2008.05621},
eprinttype = {arXiv},
eprint = {2008.05621},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2008-05621.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2008-13333,
author = {Weinan E and
Jiequn Han and
Arnulf Jentzen},
title = {Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte
Carlo to Machine Learning},
journal = {CoRR},
volume = {abs/2008.13333},
year = {2020},
url = {https://arxiv.org/abs/2008.13333},
eprinttype = {arXiv},
eprint = {2008.13333},
timestamp = {Wed, 16 Sep 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2008-13333.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2009-02327,
author = {Haijun Yu and
Xinyuan Tian and
Weinan E and
Qianxiao Li},
title = {OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized
Onsager Principle},
journal = {CoRR},
volume = {abs/2009.02327},
year = {2020},
url = {https://arxiv.org/abs/2009.02327},
eprinttype = {arXiv},
eprint = {2009.02327},
timestamp = {Fri, 18 Sep 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2009-02327.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2009-06125,
author = {Chao Ma and
Lei Wu and
Weinan E},
title = {A Qualitative Study of the Dynamic Behavior of Adaptive Gradient Algorithms},
journal = {CoRR},
volume = {abs/2009.06125},
year = {2020},
url = {https://arxiv.org/abs/2009.06125},
eprinttype = {arXiv},
eprint = {2009.06125},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2009-06125.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2009-07799,
author = {Zhong Li and
Jiequn Han and
Weinan E and
Qianxiao Li},
title = {On the Curse of Memory in Recurrent Neural Networks: Approximation
and Optimization Analysis},
journal = {CoRR},
volume = {abs/2009.07799},
year = {2020},
url = {https://arxiv.org/abs/2009.07799},
eprinttype = {arXiv},
eprint = {2009.07799},
timestamp = {Wed, 23 Sep 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2009-07799.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2009-10713,
author = {Weinan E and
Chao Ma and
Stephan Wojtowytsch and
Lei Wu},
title = {Towards a Mathematical Understanding of Neural Network-Based Machine
Learning: what we know and what we don't},
journal = {CoRR},
volume = {abs/2009.10713},
year = {2020},
url = {https://arxiv.org/abs/2009.10713},
eprinttype = {arXiv},
eprint = {2009.10713},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2009-10713.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2009-13500,
author = {Weinan E and
Stephan Wojtowytsch},
title = {A priori estimates for classification problems using neural networks},
journal = {CoRR},
volume = {abs/2009.13500},
year = {2020},
url = {https://arxiv.org/abs/2009.13500},
eprinttype = {arXiv},
eprint = {2009.13500},
timestamp = {Wed, 30 Sep 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2009-13500.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2009-14596,
author = {Weinan E},
title = {Machine Learning and Computational Mathematics},
journal = {CoRR},
volume = {abs/2009.14596},
year = {2020},
url = {https://arxiv.org/abs/2009.14596},
eprinttype = {arXiv},
eprint = {2009.14596},
timestamp = {Wed, 07 Oct 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2009-14596.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2010-05172,
author = {Yucheng Yang and
Yue Pang and
Guanhua Huang and
Weinan E},
title = {The Knowledge Graph for Macroeconomic Analysis with Alternative Big
Data},
journal = {CoRR},
volume = {abs/2010.05172},
year = {2020},
url = {https://arxiv.org/abs/2010.05172},
eprinttype = {arXiv},
eprint = {2010.05172},
timestamp = {Wed, 21 Oct 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2010-05172.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2010-05311,
author = {Yucheng Yang and
Zhong Zheng and
Weinan E},
title = {Interpretable Neural Networks for Panel Data Analysis in Economics},
journal = {CoRR},
volume = {abs/2010.05311},
year = {2020},
url = {https://arxiv.org/abs/2010.05311},
eprinttype = {arXiv},
eprint = {2010.05311},
timestamp = {Wed, 21 Oct 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2010-05311.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2010-05627,
author = {Pan Zhou and
Jiashi Feng and
Chao Ma and
Caiming Xiong and
Steven C. H. Hoi and
Weinan E},
title = {Towards Theoretically Understanding Why {SGD} Generalizes Better Than
{ADAM} in Deep Learning},
journal = {CoRR},
volume = {abs/2010.05627},
year = {2020},
url = {https://arxiv.org/abs/2010.05627},
eprinttype = {arXiv},
eprint = {2010.05627},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2010-05627.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2011-14269,
author = {Hongkang Yang and
Weinan E},
title = {Generalization and Memorization: The Bias Potential Model},
journal = {CoRR},
volume = {abs/2011.14269},
year = {2020},
url = {https://arxiv.org/abs/2011.14269},
eprinttype = {arXiv},
eprint = {2011.14269},
timestamp = {Mon, 19 Apr 2021 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2011-14269.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2012-01484,
author = {Weinan E and
Stephan Wojtowytsch},
title = {Some observations on partial differential equations in Barron and
multi-layer spaces},
journal = {CoRR},
volume = {abs/2012.01484},
year = {2020},
url = {https://arxiv.org/abs/2012.01484},
eprinttype = {arXiv},
eprint = {2012.01484},
timestamp = {Fri, 04 Dec 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2012-01484.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2012-05420,
author = {Weinan E and
Stephan Wojtowytsch},
title = {On the emergence of tetrahedral symmetry in the final and penultimate
layers of neural network classifiers},
journal = {CoRR},
volume = {abs/2012.05420},
year = {2020},
url = {https://arxiv.org/abs/2012.05420},
eprinttype = {arXiv},
eprint = {2012.05420},
timestamp = {Sat, 02 Jan 2021 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2012-05420.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-2012-12654,
author = {Tianhan Zhang and
Yaoyu Zhang and
Weinan E and
Yiguang Ju},
title = {A deep learning-based {ODE} solver for chemical kinetics},
journal = {CoRR},
volume = {abs/2012.12654},
year = {2020},
url = {https://arxiv.org/abs/2012.12654},
eprinttype = {arXiv},
eprint = {2012.12654},
timestamp = {Tue, 05 Jan 2021 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2012-12654.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jcphy/HanZE19,
author = {Jiequn Han and
Linfeng Zhang and
Weinan E},
title = {Solving many-electron Schr{\"{o}}dinger equation using deep neural
networks},
journal = {J. Comput. Phys.},
volume = {399},
year = {2019},
url = {https://doi.org/10.1016/j.jcp.2019.108929},
doi = {10.1016/J.JCP.2019.108929},
timestamp = {Wed, 19 Feb 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/jcphy/HanZE19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jmlr/LiTE19,
author = {Qianxiao Li and
Cheng Tai and
Weinan E},
title = {Stochastic Modified Equations and Dynamics of Stochastic Gradient
Algorithms {I:} Mathematical Foundations},
journal = {J. Mach. Learn. Res.},
volume = {20},
pages = {40:1--40:47},
year = {2019},
url = {http://jmlr.org/papers/v20/17-526.html},
timestamp = {Wed, 10 Jul 2019 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/jmlr/LiTE19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jns/BeckEJ19,
author = {Christian Beck and
Weinan E and
Arnulf Jentzen},
title = {Machine Learning Approximation Algorithms for High-Dimensional Fully
Nonlinear Partial Differential Equations and Second-order Backward
Stochastic Differential Equations},
journal = {J. Nonlinear Sci.},
volume = {29},
number = {4},
pages = {1563--1619},
year = {2019},
url = {https://doi.org/10.1007/s00332-018-9525-3},
doi = {10.1007/S00332-018-9525-3},
timestamp = {Thu, 14 Oct 2021 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/jns/BeckEJ19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jscic/EHJK19,
author = {Weinan E and
Martin Hutzenthaler and
Arnulf Jentzen and
Thomas Kruse},
title = {On Multilevel Picard Numerical Approximations for High-Dimensional
Nonlinear Parabolic Partial Differential Equations and High-Dimensional
Nonlinear Backward Stochastic Differential Equations},
journal = {J. Sci. Comput.},
volume = {79},
number = {3},
pages = {1534--1571},
year = {2019},
url = {https://doi.org/10.1007/s10915-018-00903-0},
doi = {10.1007/S10915-018-00903-0},
timestamp = {Thu, 14 Oct 2021 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/jscic/EHJK19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1903-02154,
author = {Weinan E and
Chao Ma and
Qingcan Wang},
title = {A Priori Estimates of the Population Risk for Residual Networks},
journal = {CoRR},
volume = {abs/1903.02154},
year = {2019},
url = {http://arxiv.org/abs/1903.02154},
eprinttype = {arXiv},
eprint = {1903.02154},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-1903-02154.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1904-04326,
author = {Weinan E and
Chao Ma and
Lei Wu},
title = {A Comparative Analysis of the Optimization and Generalization Property
of Two-layer Neural Network and Random Feature Models Under Gradient
Descent Dynamics},
journal = {CoRR},
volume = {abs/1904.04326},
year = {2019},
url = {http://arxiv.org/abs/1904.04326},
eprinttype = {arXiv},
eprint = {1904.04326},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-1904-04326.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1904-05263,
author = {Weinan E and
Chao Ma and
Qingcan Wang and
Lei Wu},
title = {Analysis of the Gradient Descent Algorithm for a Deep Neural Network
Model with Skip-connections},
journal = {CoRR},
volume = {abs/1904.05263},
year = {2019},
url = {http://arxiv.org/abs/1904.05263},
eprinttype = {arXiv},
eprint = {1904.05263},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-1904-05263.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1906-08039,
author = {Weinan E and
Chao Ma and
Lei Wu},
title = {Barron Spaces and the Compositional Function Spaces for Neural Network
Models},
journal = {CoRR},
volume = {abs/1906.08039},
year = {2019},
url = {http://arxiv.org/abs/1906.08039},
eprinttype = {arXiv},
eprint = {1906.08039},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-1906-08039.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1907-12293,
author = {Weinan E and
Yajun Zhou},
title = {A Mathematical Model for Linguistic Universals},
journal = {CoRR},
volume = {abs/1907.12293},
year = {2019},
url = {http://arxiv.org/abs/1907.12293},
eprinttype = {arXiv},
eprint = {1907.12293},
timestamp = {Thu, 01 Aug 2019 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1907-12293.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1912-06987,
author = {Weinan E and
Chao Ma and
Lei Wu},
title = {On the Generalization Properties of Minimum-norm Solutions for Over-parameterized
Neural Network Models},
journal = {CoRR},
volume = {abs/1912.06987},
year = {2019},
url = {http://arxiv.org/abs/1912.06987},
eprinttype = {arXiv},
eprint = {1912.06987},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-1912-06987.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1912-12777,
author = {Weinan E and
Chao Ma and
Lei Wu},
title = {Machine Learning from a Continuous Viewpoint},
journal = {CoRR},
volume = {abs/1912.12777},
year = {2019},
url = {http://arxiv.org/abs/1912.12777},
eprinttype = {arXiv},
eprint = {1912.12777},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-1912-12777.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/cphysics/WangZHE18,
author = {Han Wang and
Linfeng Zhang and
Jiequn Han and
Weinan E},
title = {DeePMD-kit: {A} deep learning package for many-body potential energy
representation and molecular dynamics},
journal = {Comput. Phys. Commun.},
volume = {228},
pages = {178--184},
year = {2018},
url = {https://doi.org/10.1016/j.cpc.2018.03.016},
doi = {10.1016/J.CPC.2018.03.016},
timestamp = {Fri, 25 Dec 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/cphysics/WangZHE18.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/nips/ZhangHWSCE18,
author = {Linfeng Zhang and
Jiequn Han and
Han Wang and
Wissam Saidi and
Roberto Car and
Weinan E},
editor = {Samy Bengio and
Hanna M. Wallach and
Hugo Larochelle and
Kristen Grauman and
Nicol{\`{o}} Cesa{-}Bianchi and
Roman Garnett},
title = {End-to-end Symmetry Preserving Inter-atomic Potential Energy Model
for Finite and Extended Systems},
booktitle = {Advances in Neural Information Processing Systems 31: Annual Conference
on Neural Information Processing Systems 2018, NeurIPS 2018, December
3-8, 2018, Montr{\'{e}}al, Canada},
pages = {4441--4451},
year = {2018},
url = {https://proceedings.neurips.cc/paper/2018/hash/e2ad76f2326fbc6b56a45a56c59fafdb-Abstract.html},
timestamp = {Mon, 16 May 2022 15:41:51 +0200},
biburl = {https://dblp.org/rec/conf/nips/ZhangHWSCE18.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/nips/WuME18,
author = {Lei Wu and
Chao Ma and
Weinan E},
editor = {Samy Bengio and
Hanna M. Wallach and
Hugo Larochelle and
Kristen Grauman and
Nicol{\`{o}} Cesa{-}Bianchi and
Roman Garnett},
title = {How {SGD} Selects the Global Minima in Over-parameterized Learning:
{A} Dynamical Stability Perspective},
booktitle = {Advances in Neural Information Processing Systems 31: Annual Conference
on Neural Information Processing Systems 2018, NeurIPS 2018, December
3-8, 2018, Montr{\'{e}}al, Canada},
pages = {8289--8298},
year = {2018},
url = {https://proceedings.neurips.cc/paper/2018/hash/6651526b6fb8f29a00507de6a49ce30f-Abstract.html},
timestamp = {Thu, 21 Jan 2021 00:00:00 +0100},
biburl = {https://dblp.org/rec/conf/nips/WuME18.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1802-09707,
author = {Lei Wu and
Zhanxing Zhu and
Cheng Tai and
Weinan E},
title = {Understanding and Enhancing the Transferability of Adversarial Examples},
journal = {CoRR},
volume = {abs/1802.09707},
year = {2018},
url = {http://arxiv.org/abs/1802.09707},
eprinttype = {arXiv},
eprint = {1802.09707},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1802-09707.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1807-00297,
author = {Weinan E and
Qingcan Wang},
title = {Exponential Convergence of the Deep Neural Network Approximation for
Analytic Functions},
journal = {CoRR},
volume = {abs/1807.00297},
year = {2018},
url = {http://arxiv.org/abs/1807.00297},
eprinttype = {arXiv},
eprint = {1807.00297},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1807-00297.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1807-01083,
author = {Weinan E and
Jiequn Han and
Qianxiao Li},
title = {A Mean-Field Optimal Control Formulation of Deep Learning},
journal = {CoRR},
volume = {abs/1807.01083},
year = {2018},
url = {http://arxiv.org/abs/1807.01083},
eprinttype = {arXiv},
eprint = {1807.01083},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1807-01083.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1808-04258,
author = {Chao Ma and
Jianchun Wang and
Weinan E},
title = {Model Reduction with Memory and the Machine Learning of Dynamical
Systems},
journal = {CoRR},
volume = {abs/1808.04258},
year = {2018},
url = {http://arxiv.org/abs/1808.04258},
eprinttype = {arXiv},
eprint = {1808.04258},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-1808-04258.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1809-10188,
author = {Linfeng Zhang and
Weinan E and
Lei Wang},
title = {Monge-Amp{\`{e}}re Flow for Generative Modeling},
journal = {CoRR},
volume = {abs/1809.10188},
year = {2018},
url = {http://arxiv.org/abs/1809.10188},
eprinttype = {arXiv},
eprint = {1809.10188},
timestamp = {Fri, 05 Oct 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1809-10188.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1810-06397,
author = {Weinan E and
Chao Ma and
Lei Wu},
title = {A Priori Estimates of the Generalization Error for Two-layer Neural
Networks},
journal = {CoRR},
volume = {abs/1810.06397},
year = {2018},
url = {http://arxiv.org/abs/1810.06397},
eprinttype = {arXiv},
eprint = {1810.06397},
timestamp = {Thu, 26 Nov 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-1810-06397.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1810-11890,
author = {Linfeng Zhang and
De{-}Ye Lin and
Han Wang and
Roberto Car and
Weinan E},
title = {Active Learning of Uniformly Accurate Inter-atomic Potentials for
Materials Simulation},
journal = {CoRR},
volume = {abs/1810.11890},
year = {2018},
url = {http://arxiv.org/abs/1810.11890},
eprinttype = {arXiv},
eprint = {1810.11890},
timestamp = {Mon, 22 Jun 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1810-11890.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1811-01558,
author = {Qianxiao Li and
Cheng Tai and
Weinan E},
title = {Stochastic Modified Equations and Dynamics of Stochastic Gradient
Algorithms {I:} Mathematical Foundations},
journal = {CoRR},
volume = {abs/1811.01558},
year = {2018},
url = {http://arxiv.org/abs/1811.01558},
eprinttype = {arXiv},
eprint = {1811.01558},
timestamp = {Thu, 22 Nov 2018 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-1811-01558.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jmlr/LiCTE17,
author = {Qianxiao Li and
Long Chen and
Cheng Tai and
Weinan E},
title = {Maximum Principle Based Algorithms for Deep Learning},
journal = {J. Mach. Learn. Res.},
volume = {18},
pages = {165:1--165:29},
year = {2017},
url = {http://jmlr.org/papers/v18/17-653.html},
timestamp = {Wed, 10 Jul 2019 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/jmlr/LiCTE17.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/icml/LiTE17,
author = {Qianxiao Li and
Cheng Tai and
Weinan E},
editor = {Doina Precup and
Yee Whye Teh},
title = {Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms},
booktitle = {Proceedings of the 34th International Conference on Machine Learning,
{ICML} 2017, Sydney, NSW, Australia, 6-11 August 2017},
series = {Proceedings of Machine Learning Research},
volume = {70},
pages = {2101--2110},
publisher = {{PMLR}},
year = {2017},
url = {http://proceedings.mlr.press/v70/li17f.html},
timestamp = {Wed, 29 May 2019 08:41:45 +0200},
biburl = {https://dblp.org/rec/conf/icml/LiTE17.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/sigir/YanZE17,
author = {Rui Yan and
Dongyan Zhao and
Weinan E},
editor = {Noriko Kando and
Tetsuya Sakai and
Hideo Joho and
Hang Li and
Arjen P. de Vries and
Ryen W. White},
title = {Joint Learning of Response Ranking and Next Utterance Suggestion in
Human-Computer Conversation System},
booktitle = {Proceedings of the 40th International {ACM} {SIGIR} Conference on
Research and Development in Information Retrieval, Shinjuku, Tokyo,
Japan, August 7-11, 2017},
pages = {685--694},
publisher = {{ACM}},
year = {2017},
url = {https://doi.org/10.1145/3077136.3080843},
doi = {10.1145/3077136.3080843},
timestamp = {Sat, 31 Aug 2019 01:00:00 +0200},
biburl = {https://dblp.org/rec/conf/sigir/YanZE17.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/EHJ17,
author = {Weinan E and
Jiequn Han and
Arnulf Jentzen},
title = {Deep learning-based numerical methods for high-dimensional parabolic
partial differential equations and backward stochastic differential
equations},
journal = {CoRR},
volume = {abs/1706.04702},
year = {2017},
url = {http://arxiv.org/abs/1706.04702},
eprinttype = {arXiv},
eprint = {1706.04702},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/EHJ17.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/WuZE17,
author = {Lei Wu and
Zhanxing Zhu and
Weinan E},
title = {Towards Understanding Generalization of Deep Learning: Perspective
of Loss Landscapes},
journal = {CoRR},
volume = {abs/1706.10239},
year = {2017},
url = {http://arxiv.org/abs/1706.10239},
eprinttype = {arXiv},
eprint = {1706.10239},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/WuZE17.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/HanJE17,
author = {Jiequn Han and
Arnulf Jentzen and
Weinan E},
title = {Overcoming the curse of dimensionality: Solving high-dimensional partial
differential equations using deep learning},
journal = {CoRR},
volume = {abs/1707.02568},
year = {2017},
url = {http://arxiv.org/abs/1707.02568},
eprinttype = {arXiv},
eprint = {1707.02568},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/HanJE17.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/ZhangHWCE17,
author = {Linfeng Zhang and
Jiequn Han and
Han Wang and
Roberto Car and
Weinan E},
title = {Deep Potential Molecular Dynamics: a scalable model with the accuracy
of quantum mechanics},
journal = {CoRR},
volume = {abs/1707.09571},
year = {2017},
url = {http://arxiv.org/abs/1707.09571},
eprinttype = {arXiv},
eprint = {1707.09571},
timestamp = {Mon, 22 Jun 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/ZhangHWCE17.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1709-05963,
author = {Christian Beck and
Weinan E and
Arnulf Jentzen},
title = {Machine learning approximation algorithms for high-dimensional fully
nonlinear partial differential equations and second-order backward
stochastic differential equations},
journal = {CoRR},
volume = {abs/1709.05963},
year = {2017},
url = {http://arxiv.org/abs/1709.05963},
eprinttype = {arXiv},
eprint = {1709.05963},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1709-05963.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1710-00211,
author = {Weinan E and
Bing Yu},
title = {The Deep Ritz method: {A} deep learning-based numerical algorithm
for solving variational problems},
journal = {CoRR},
volume = {abs/1710.00211},
year = {2017},
url = {http://arxiv.org/abs/1710.00211},
eprinttype = {arXiv},
eprint = {1710.00211},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1710-00211.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1710-09513,
author = {Qianxiao Li and
Long Chen and
Cheng Tai and
Weinan E},
title = {Maximum Principle Based Algorithms for Deep Learning},
journal = {CoRR},
volume = {abs/1710.09513},
year = {2017},
url = {http://arxiv.org/abs/1710.09513},
eprinttype = {arXiv},
eprint = {1710.09513},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1710-09513.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1712-03461,
author = {Linfeng Zhang and
Han Wang and
Weinan E},
title = {Reinforced dynamics for enhanced sampling in large atomic and molecular
systems. I. Basic Methodology},
journal = {CoRR},
volume = {abs/1712.03461},
year = {2017},
url = {http://arxiv.org/abs/1712.03461},
eprinttype = {arXiv},
eprint = {1712.03461},
timestamp = {Mon, 22 Jun 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1712-03461.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1712-03641,
author = {Han Wang and
Linfeng Zhang and
Jiequn Han and
Weinan E},
title = {DeePMD-kit: {A} deep learning package for many-body potential energy
representation and molecular dynamics},
journal = {CoRR},
volume = {abs/1712.03641},
year = {2017},
url = {http://arxiv.org/abs/1712.03641},
eprinttype = {arXiv},
eprint = {1712.03641},
timestamp = {Mon, 22 Jun 2020 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1712-03641.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jmlr/TaiE16,
author = {Cheng Tai and
Weinan E},
title = {Multiscale Adaptive Representation of Signals: I. The Basic Framework},
journal = {J. Mach. Learn. Res.},
volume = {17},
pages = {140:1--140:38},
year = {2016},
url = {http://jmlr.org/papers/v17/15-072.html},
timestamp = {Wed, 10 Jul 2019 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/jmlr/TaiE16.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/cdc/WangLEC16,
author = {Chu Wang and
Qianxiao Li and
Weinan E and
Bernard Chazelle},
title = {Noisy Hegselmann-Krause systems: Phase transition and the 2R-conjecture},
booktitle = {55th {IEEE} Conference on Decision and Control, {CDC} 2016, Las Vegas,
NV, USA, December 12-14, 2016},
pages = {2632--2637},
publisher = {{IEEE}},
year = {2016},
url = {https://doi.org/10.1109/CDC.2016.7798659},
doi = {10.1109/CDC.2016.7798659},
timestamp = {Fri, 04 Mar 2022 13:29:43 +0100},
biburl = {https://dblp.org/rec/conf/cdc/WangLEC16.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:journals/corr/TaiXWE15,
author = {Cheng Tai and
Tong Xiao and
Xiaogang Wang and
Weinan E},
editor = {Yoshua Bengio and
Yann LeCun},
title = {Convolutional neural networks with low-rank regularization},
booktitle = {4th International Conference on Learning Representations, {ICLR} 2016,
San Juan, Puerto Rico, May 2-4, 2016, Conference Track Proceedings},
year = {2016},
url = {http://arxiv.org/abs/1511.06067},
timestamp = {Thu, 15 Apr 2021 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/TaiXWE15.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/HanE16,
author = {Jiequn Han and
Weinan E},
title = {Deep Learning Approximation for Stochastic Control Problems},
journal = {CoRR},
volume = {abs/1611.07422},
year = {2016},
url = {http://arxiv.org/abs/1611.07422},
eprinttype = {arXiv},
eprint = {1611.07422},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/HanE16.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/TaiE15,
author = {Cheng Tai and
Weinan E},
title = {Multiscale Adaptive Representation of Signals: I. The Basic Framework},
journal = {CoRR},
volume = {abs/1507.04835},
year = {2015},
url = {http://arxiv.org/abs/1507.04835},
eprinttype = {arXiv},
eprint = {1507.04835},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/TaiE15.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/WangWES15,
author = {Chu Wang and
Yingfei Wang and
Weinan E and
Robert E. Schapire},
title = {Functional Frank-Wolfe Boosting for General Loss Functions},
journal = {CoRR},
volume = {abs/1510.02558},
year = {2015},
url = {http://arxiv.org/abs/1510.02558},
eprinttype = {arXiv},
eprint = {1510.02558},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/WangWES15.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/LiTE15,
author = {Qianxiao Li and
Cheng Tai and
Weinan E},
title = {Dynamics of Stochastic Gradient Algorithms},
journal = {CoRR},
volume = {abs/1511.06251},
year = {2015},
url = {http://arxiv.org/abs/1511.06251},
eprinttype = {arXiv},
eprint = {1511.06251},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/LiTE15.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{DBLP:conf/ciss/TianW14,
author = {Haoshu Tian and
Weinan E},
title = {Fire sale in financial networks},
booktitle = {48th Annual Conference on Information Sciences and Systems, {CISS}
2014, Princeton, NJ, USA, March 19-21, 2014},
pages = {1--5},
publisher = {{IEEE}},
year = {2014},
url = {https://doi.org/10.1109/CISS.2014.6814162},
doi = {10.1109/CISS.2014.6814162},
timestamp = {Wed, 16 Oct 2019 14:14:51 +0200},
biburl = {https://dblp.org/rec/conf/ciss/TianW14.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jcphy/LinSE13,
author = {Lin Lin and
Sihong Shao and
Weinan E},
title = {Efficient iterative method for solving the Dirac-Kohn-Sham density
functional theory},
journal = {J. Comput. Phys.},
volume = {245},
pages = {205--217},
year = {2013},
url = {https://doi.org/10.1016/j.jcp.2013.03.030},
doi = {10.1016/J.JCP.2013.03.030},
timestamp = {Wed, 19 Feb 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/jcphy/LinSE13.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/actanum/AbdulleEEV12,
author = {Assyr Abdulle and
Weinan E and
Bj{\"{o}}rn Engquist and
Eric Vanden{-}Eijnden},
title = {The heterogeneous multiscale method},
journal = {Acta Numer.},
volume = {21},
pages = {1--87},
year = {2012},
url = {https://doi.org/10.1017/S0962492912000025},
doi = {10.1017/S0962492912000025},
timestamp = {Fri, 25 Dec 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/actanum/AbdulleEEV12.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/jcphy/LinLYE12,
author = {Lin Lin and
Jianfeng Lu and
Lexing Ying and
Weinan E},
title = {Adaptive local basis set for Kohn-Sham density functional theory in
a discontinuous Galerkin framework {I:} Total energy calculation},
journal = {J. Comput. Phys.},
volume = {231},
number = {4},
pages = {2140--2154},
year = {2012},
url = {https://doi.org/10.1016/j.jcp.2011.11.032},
doi = {10.1016/J.JCP.2011.11.032},
timestamp = {Wed, 19 Feb 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/jcphy/LinLYE12.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
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author = {Lin Lin and
Jianfeng Lu and
Lexing Ying and
Weinan E},
title = {Optimized local basis set for Kohn-Sham density functional theory},
journal = {J. Comput. Phys.},
volume = {231},
number = {13},
pages = {4515--4529},
year = {2012},
url = {https://doi.org/10.1016/j.jcp.2012.03.009},
doi = {10.1016/J.JCP.2012.03.009},
timestamp = {Wed, 19 Feb 2020 00:00:00 +0100},
biburl = {https://dblp.org/rec/journals/jcphy/LinLYE12a.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/corr/abs-1204-6376,
author = {Weinan E and
Jianfeng Lu and
Yuan Yao},
title = {The Landscape of Complex Networks},
journal = {CoRR},
volume = {abs/1204.6376},
year = {2012},
url = {http://arxiv.org/abs/1204.6376},
eprinttype = {arXiv},
eprint = {1204.6376},
timestamp = {Mon, 13 Aug 2018 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1204-6376.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/scholarpedia/EL11,
author = {Weinan E and
Jianfeng Lu},
title = {Multiscale modeling},
journal = {Scholarpedia},
volume = {6},
number = {10},
pages = {11527},
year = {2011},
url = {https://doi.org/10.4249/scholarpedia.11527},
doi = {10.4249/SCHOLARPEDIA.11527},
timestamp = {Thu, 23 May 2019 01:00:00 +0200},
biburl = {https://dblp.org/rec/journals/scholarpedia/EL11.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DBLP:journals/siamsc/LinYLYE11,
author = {Lin Lin and
Chao Yang and
Jianfeng Lu and
Lexing Ying and
Weinan E},
title = {A Fast Parallel Algorithm for Selected Inversion of Structured Sparse
Matrices with Application to 2D Electronic Structure Calculations},
journal = {{SIAM} J. Sci. Comput.},
volume = {33},
number = {3},
pages = {1329--1351},
year = {2011},
url = {https://doi.org/10.1137/09077432X},
doi = {10.1137/09077432X},
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Rohit Patra and
Xiang Zhou and
Weinan E},
editor = {S. Jain and
Roy R. Creasey Jr. and
Jan Himmelspach and
K. Preston White and
Michael C. Fu},
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publisher = {{IEEE}},
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bibsource = {dblp computer science bibliography, https://dblp.org}
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