JENTZEN, Arnulf

Presidential Chair Professor

Education Background

PhD in Mathematics, Goethe University Frankfurt, 2009

Diploma in Mathematics, Goethe University Frankfurt, 2007

Research Field
Machine learning approximation algorithms, computational stochastics, numerical analysis for high dimensional partial differential equations (PDEs), stochastic analysis, and computational finance
Personal Website
Email
ajentzen@cuhk.edu.cn
Biography

Professor Arnulf JENTZEN is a Presidential Chair Professor at The Chinese University of Hong Kong, Shenzhen. In addition, since 2019 he has been employed as a Professor for Applied Mathematics at the Faculty of Mathematics and Computer Science in the University of Münster. He received his Diploma (2007) and PhD (2009) in Mathematics from Goethe University Frankfurt.

The core research topics of Professor Arnulf Jentzen are machine learning approximation algorithms, computational stochastics, numerical analysis for high dimensional partial differential equations (PDEs), stochastic analysis, and computational finance. He is particularly interested in deep learning based algorithms for high dimensional approximation problems and different kinds of differential equations.

Professor Arnulf Jentzen has received a number of awards for his research contributions. In particular, he is the winner of the 2018 Joseph F. Traub Information-Based Complexity Young Researcher Award and in 2020 he has been awarded the Felix Klein Prize of the European Mathematical Society (EMS). He has also successfully obtained several research grants for his research activities. Professor Arnulf Jentzen has been invited to work as editor of many international top magazines, such as the Annals of Applied Probability (AAP), Communications in Computational Physics (CiCP), Communications in Mathematical Sciences (CMS), the Journal of Complexity (JoC), the Journal of Mathematical Analysis and Applications (JMAA), the SIAM/ASA Journal on Uncertainty Quantification (JUQ), the SIAM Journal of Scientific Computing (SISC), and the SIAM Journal on Numerical Analysis (SINUM). Since he has received his PhD in October 2009, he has been invited to more than 100 research talks and 5 minicourses. In addition, he has collaboratively organized a series of workshops, minisymposia, and programmes, respectively.

Academic Publications

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.

A complete list of publications can be found at Professor Arnulf JENTZEN's personal website.