機器學習

數學理論與科學應用

20210115 Issue #19

 

本文預覽

  • 作者:鄂維南  Weinan E
    • 作者簡介

鄂維南是普林斯頓大學數學系教授,應用數學與計算數學博士學程主任,同時也是運籌學與金融工程學系的合聘教授。以他在應用數學和科學計算的相關領域方面的工作而聞名,特別是在非線性隨機偏微分方程、計算流體動力學、計算化學和機器學習等方面。

 

  •  譯者:葉千雅
    • 譯者簡介

葉千雅是新竹高工數學科教師。

 

  • 本文出處
    本文譯自“Machine Learning: Mathematical Theory and Scientific Applications”, Notices of the American Mathematical Society 66 (2019) No.11, AMS。
    感謝AMS 同意轉載翻譯。同文是2019 年7 月15 日在西班牙瓦倫西亞舉行的第九屆國際工業和應用數學大會(ICIAM 2019)中,本文作者於彼得亨利希獎(Peter Henrici Prize)演講的筆錄。

 

  • 延伸閱讀
    • 基於機器學習演算法求解高維度控制問題是由作者首先提出的。參見Jiequn Han, Weinan E,“Deep Learning Approximation for Stochastic Control Problems”, accepted, NIPS Workshop on Deep Reinforcement Learning (2016)。
    • 作者也是首位提出基於機器學習演算法求解高維度非線性偏微分方程。參見Weinan E, Jiequn Han, Arnulf Jentzen,“Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations”, Communications in Mathematics and Statistics 5 (2017)。
    • 作者並架設及管理以下的網站,網站內收集許多機器學習的數學理論,以及運用機器學習在處理多尺度建模問題上。
      https://web.math.princeton.edu/~weinan/

 

  • 參考資料

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[16] Wang H, Zhang LF, Han J, and E W, DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics, Comput. Phys. ACKNOWLEDGMENT. Machine learning is an area in which young people are playing a particularly active role. This is also reflected in the work reported here. In particular, I am grateful to my young collaborators for their contribution to the work reported here: Jiequn Han, Arnulf Jentzen, Qianxiao Li, Chao Ma, Zheng Ma, Cheng Tai, Han Wang, Qingcan Wang, Lei Wu, Linfeng Zhang, and Yajun Zhou. I am also grateful to Reza Malek-Madani for his suggestions, which helped to im- prove the draft. Comm., vol. 228, pp. 178–184, 2018.
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