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个人简介
My current work focuses on the mathematical theory of machine learning and integrating machine learning with multi-scale modeling.
Research summary: My work draws inspiration from various disciplines of sciences and has made an impact in fluid dynamics, chemistry, material sciences, and soft condensed matter physics. I have contributed to the resolution of some long standing scientific problems such as the Burgers turbulence problem (which was the original motivation of Burgers for proposing the well-known Burgers equation), the Cauchy-Born rule for crystalline solids (which indeed dates back to Cauchy, and provides a microscopic foundation for the elasticity theory), and the moving contact line problem (which is still largely open). A common theme is to try bringing clarity to scientific issues through mathematics. A second theme is multi-scale and/or multi-physics problems. I have also worked on building the mathematical framework and finding effective numerical algorithms for modeling rare events which is a very difficult class of problems involving multiple time scales (string method, minimum action methods, transition path theory, etc). I have also worked on multiscale analysis and algorithms (e.g. the heterogeneous multi-scale method) for stochastic simulation algorithms, homogenization problems, problems with multiple time scales, complex fluids, etc. My book (Principles of Multi-Scale Modeling, Cambridge Univ Press) provides a broad introduction to this subject. A third theme is to develop and analyze algorithms in general. In computational fluid mechanics, I was involved in analyzing and developing vorticity-based methods, the project method and the gauge method. In density functional theory (DFT), my collaborators and I have developed the PEXSI algorithm, which is so far the most efficient algorithm for DFT.
Research summary: My work draws inspiration from various disciplines of sciences and has made an impact in fluid dynamics, chemistry, material sciences, and soft condensed matter physics. I have contributed to the resolution of some long standing scientific problems such as the Burgers turbulence problem (which was the original motivation of Burgers for proposing the well-known Burgers equation), the Cauchy-Born rule for crystalline solids (which indeed dates back to Cauchy, and provides a microscopic foundation for the elasticity theory), and the moving contact line problem (which is still largely open). A common theme is to try bringing clarity to scientific issues through mathematics. A second theme is multi-scale and/or multi-physics problems. I have also worked on building the mathematical framework and finding effective numerical algorithms for modeling rare events which is a very difficult class of problems involving multiple time scales (string method, minimum action methods, transition path theory, etc). I have also worked on multiscale analysis and algorithms (e.g. the heterogeneous multi-scale method) for stochastic simulation algorithms, homogenization problems, problems with multiple time scales, complex fluids, etc. My book (Principles of Multi-Scale Modeling, Cambridge Univ Press) provides a broad introduction to this subject. A third theme is to develop and analyze algorithms in general. In computational fluid mechanics, I was involved in analyzing and developing vorticity-based methods, the project method and the gauge method. In density functional theory (DFT), my collaborators and I have developed the PEXSI algorithm, which is so far the most efficient algorithm for DFT.
研究兴趣
论文共 427 篇作者统计合作学者相似作者
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CoRR (2024)
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CoRR (2024)
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Communications on Applied Mathematics and Computationno. 2 (2024): 1-28
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICAno. 14 (2024): e2308668121-e2308668121
biorxiv(2024)
Boshen Zeng, Sian Chen, Xinxin Liu, Changhong Chen, Bin Deng,Xiaoxu Wang,Zhifeng Gao, Yuzhi Zhang,Weinan E,Linfeng Zhang
arxiv(2024)
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Hongkang Yang,Zehao Lin, Wenjin Wang, Hao Wu, Zhiyu Li, Bo Tang, Wenqiang Wei, Jinbo Wang, Zeyun Tang,Shichao Song,Chenyang Xi, Yu Yu,
arxiv(2024)
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COMBUSTION AND FLAME (2024): 113286
ANGEWANDTE CHEMIE-INTERNATIONAL EDITIONno. 27 (2024): e202405379-e202405379
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作者统计
#Papers: 433
#Citation: 27391
H-Index: 81
G-Index: 154
Sociability: 6
Diversity: 1
Activity: 4
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