no code implementations • 2 Dec 2021 • Chengyuan Han, Hannes Hilger, Eva Mix, Philipp C. Böttcher, Mark Reyers, Christian Beck, Dirk Witthaut, Leonardo Rydin Gorjão
Electricity markets are central for the coordination of electric power generation.
no code implementations • 20 Oct 2021 • Benedikt Sohmen, Christian Beck, Tilo Seydel, Ingo Hoffmann, Bianca Hermann, Mark Nüesch, Marco Grimaldo, Frank Schreiber, Steffen Wolf, Felix Roosen-Runge, Thorsten Hugel
Nano- and picosecond dynamics have been assigned to local fluctuations, while slower dynamics have been attributed to larger conformational changes.
no code implementations • 22 Dec 2020 • Christian Beck, Martin Hutzenthaler, Arnulf Jentzen, Benno Kuckuck
It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs).
no code implementations • 2 Dec 2020 • Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, Ariel Neufeld
In this article we introduce and study a deep learning based approximation algorithm for solutions of stochastic partial differential equations (SPDEs).
no code implementations • 8 Jul 2019 • Christian Beck, Sebastian Becker, Patrick Cheridito, Arnulf Jentzen, Ariel Neufeld
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning.
no code implementations • 1 Jun 2018 • Christian Beck, Sebastian Becker, Philipp Grohs, Nor Jaafari, Arnulf Jentzen
Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations (PDEs) associated to them have been widely used in models from engineering, finance, and the natural sciences.
no code implementations • 18 Sep 2017 • Christian Beck, Weinan E, Arnulf Jentzen
The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio.