JENTZEN, Arnulf

教授

教育背景

博士(法兰克福大学)

学士(法兰克福大学)

研究领域
机器学习近似算法,计算随机学,高维偏微分方程的数值分析,随机分析和计算金融
个人网站
电子邮件
ajentzen@cuhk.edu.cn
个人简介

Arnulf Jentzen现为香港中文大学(深圳)教授,同时也是明斯特大学数学与计算机科学学院的教授。他分别于2007年与2009年获德国法兰克福大学数学学士学位与博士学位。

Arnulf Jentzen教授的核心研究课题是机器学习近似演算法、计算随机学、高维偏微分方程的数值分析、随机分析和计算金融学。他对基于深度学习的高维优化、控制问题的算法和各种微分方程的随机近似演算法特别感兴趣。

Arnulf Jentzen教授在研究方面获得了许多奖项。他是2018年Joseph F. Traub基于信息复杂性研究的青年研究学家奖获得者。于2020年,他被欧洲数学学会授予菲利克斯克莱因奖项,不仅如此,他的研究活动已经吸引了无数研究资助。Arnulf Jentzen教授曾受邀担任多部国际顶尖杂志的编辑,比如《应用概率论年报》(AAP)、《计算物理通讯》(CMS)、《复杂学杂志》(JoC)、《数学分析与应用杂志》(JMAA)、SIAM/ASA《不确定性量化期刊》(JUQ)、SIAM《科学计算期刊》(SISC)、SIAM《数值分析期刊》(SINUM)。自2009年10月获得博士学位以来,他已经受邀讲授超过100场研究讲座和5门小型课程,合作组织了一系列研讨会。

学术著作

1. Hutzenthaler, M. & Jentzen, A., On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficients. Ann. Probab. 48 (2020), no. 1, 53–93. arXiv:1401.0295 (2014), 41 pages, http://arxiv.org/abs/1401.0295.

2.  Hutzenthaler, M., Jentzen, A., Kruse, T., Nguyen, T., A proof that rectified deep neural networks  overcome the curse of dimensionality in the numerical approximation of semilinear heat equations. SN PDE 1 (2020), no. 10, 1–34. arXiv:1901.10854 (2019), 29 pages,  https://arxiv.org/abs/1901.10854.

3.  Fehrman, B., Gess, B., Jentzen, A., Convergence rates for the stochastic gradient descent method for non-convex objective functions. J. Mach. Learn. Res. 21 (2020), Paper No. 136, 1–48. arXiv:1904.01517 (2019), 52 pages, https://arxiv.org/abs/1904.01517.

4.  Hutzenthaler, M., Jentzen, A., Kruse, T., Nguyen, T. A., & von Wurstemberger, P., Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations. Proc. R. Soc. A 476 (2020), no. 2244, 20190630, 25 pp. arXiv:1807.01212 (2018), 27 pages, https://arxiv.org/abs/1903.05985.

5.  Becker, S., Cheridito, P., & Jentzen, A., Deep optimal stopping. J. Mach. Learn. Res. 20 (2019), Paper No. 74, 1–25. arXiv:1804.05394 (2018), 18 pages, https://arxiv.org/abs/1804.05394.

6.  Grohs, P., Hornung, F., Jentzen, A., von Wurstemberger, P., A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. arXiv:1807.01212  (2018), 124 pages, https://arxiv.org/abs/1809.02362. Accepted in Mem. Amer. Math. Soc.

7.  Han, J., Jentzen, A., & E, W., Solving high-dimensional partial differential equations using deep learning. Proc. Natl. Acad. Sci. USA 115 (2018), no. 34, 8505–8510. arXiv:1707.02568 (2017), 13 pages, https://arxiv.org/abs/1707.02568.

8.  E, W., Han, J., & Jentzen, A., Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Commun. Math. Stat. 5 (2017), no. 4,  349–380.  arXiv:1706.04702  (2017), 39 pages, https://arxiv.org/abs/1706.04702.

9.  Hairer, M., Hutzenthaler, M., & Jentzen, A., Loss of regularity for Kolmogorov equations. Ann. Probab. 43 (2015), no. 2, 468–527. arXiv:1209.6035 (2015), 62 pages, https://arxiv.org/abs/1209.6035.

10.  Hutzenthaler, M., Jentzen, A., & Kloeden, P. E., Strong convergence of an explicit numerical method for SDEs with non-globally Lipschitz continuous  coefficients. Ann. Appl. Probab. 22 (2012), no. 4, 1611-1641. arXiv:1010.3756 (Awarded a second prize of the 15th Leslie Fox Prize in Numerical Analysis (Manchester, UK, June 2011).) arXiv:1010.3756 (2012), 32 pages, https://arxiv.org/abs/1010.3756.

11.  Hutzenthaler, M., Jentzen, A., & Kloeden, P. E., Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. Proc. R. Soc. A 467 (2011), no. 2130, 1563–1576. arXiv:0905.0273 (2011), 32 pages, https://arxiv.org/abs/0905.0273.

 

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