CUHK-SZ
email: philippevw (at) cuhk.edu.cn
Links: [Profile on GoogleScholar] [Profile on ResearchGate]
I hold a PhD in Mathematics from ETH Zurich and am a postdoctoral researcher at the Chinese University of Hong Kong, Shenzhen.
My work lies at the intersection of mathematics and deep learning, with a dual focus: firstly, to deepen the theoretical understanding of deep learning through mathematical theory, and secondly, to innovate new deep learning methods for tackling numerical mathematics problems.
Short CV
| 11/2021 - | Visiting researcher at the Chinese University of Hong Kong, Shenzhen in the research group of Prof. Arnulf Jentzen | |||
| 2018 - 2024 | PhD in Mathematics at ETH Zurich under the supervision of Prof. Patrick Cheridito and Prof. Arnulf Jentzen | |||
| 05/2018 - 06/2018 | Research assistant at ETH Zurich in the group of Prof. Arnulf Jentzen | |||
| 2016 - 2018 | Master of Science in Mathematics, ETH Zurich, Switzerland | |||
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Overall Grade Point Average: 5.96 (out of 6) mit Auszeichnung / summa cum laude |
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| Fall 2015 | Exchange semester at Princeton University | |||
| 2012 - 2015 | Bachelor of Science in Mathematics, ETH Zurich, Switzerland | |||
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Overall Grade Point Average: 5.88 (out of 6) mit Auszeichnung / summa cum laude |
Awards
- ETH Medal (2019) for an outstanding Master's thesis
Invited talks
| 05/2018 |
Stochastic optimization seminar at ETH Zurich. Error analysis and lower error bounds for SGD. |
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| 05/2019 |
SMAI, Guidel Plages. Overcoming the curse of dimensionality with DNNs: Theoretical approximation results for PDEs. [Slides] |
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| 07/2019 |
International Conference on Computational
Finance, A Coruna. Overcoming the curse of dimensionality with Deep Learning: Methods and theoretical results for PDEs. [Slides] |
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| 06/2022 |
11th World Congress of
Bachelier Finance Society, Hong Kong. Overcoming the curse of dimensionality in the approximation of semilinear Black-Scholes PDEs [Slides] |
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| 06/2023 |
Foundations of Computational Mathematics, Paris.
Learning the random variables: Combining Monte Carlo simulations with machine learning. [Slides] |
Publications and Accepted Preprints
- Becker, S., Jentzen, A., Müller, M. S., & von Wurstemberger, P., Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing. Math. Financ. 34 (2024). [arXiv].
- Becker, S., Braunwarth, R., Hutzenthaler, M., Jentzen, A., von Wurstemberger, P., Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. Commun. Comput. Phys. 28 (2020). [arXiv].
- Hutzenthaler, M., Jentzen, A., von Wurstemberger, P., Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks. Electron. J. Probab. 25 (2020). [arXiv].
- 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. Mem. Amer. Math. Soc. 248 (2023). [arXiv].
- 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). [arXiv].
- Jentzen, A., von Wurstemberger, P., Lower error bounds for the stochastic gradient descent optimization algorithm: Sharp convergence rates for slowly and fast decaying learning rates. J. Complexity 57 (2020). [arXiv].
- Jentzen, A., Kuckuck, B., Neufeld, A., von Wurstemberger, P., Strong error analysis for stochastic gradient descent optimization algorithms. IMA J. Numer. Anal. (2020). [arXiv].
Preprints
- Gallon, D., von Wurstemberger, P., Cheridito, P., Jentzen, A., Physics-informed diffusion models in spectral space. [arXiv] (2026).
- Gallon, D., Jentzen, A., von Wurstemberger, P., An overview of diffusion models for generative artificial intelligence. [arXiv] (2024).
- Gonon, L., Jentzen, A., Kuckuck, B., Liang, S., Riekert, A., von Wurstemberger, P., An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning. [arXiv] (2024).
- Jentzen, A., Riekert, A., von Wurstemberger, P., Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations. [arXiv] (2023).
- Beneventano, P., Cheridito, P., Jentzen, A., von Wurstemberger, P., High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations. [arXiv] (2020).
Books and Lecture Notes
- Jentzen, A., Kuckuck, B., Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory. [arXiv] (2023).