135 citations · 872 across the 21 of their papers we have counts for
9 papers · 1 filter
An efficient Monte Carlo scheme for Zakai equations
Christian Beck, Sebastian Becker, Patrick Cheridito +2
In this paper we develop a numerical method for efficiently approximating solutions of certain Zakai equations in high dimensions. The key idea is to transform a given Zakai SPDE i…
Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions
Victor Boussange, Sebastian Becker, Arnulf Jentzen +2
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications…
Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing
Sebastian Becker, Arnulf Jentzen, Marvin S. Müller +1
In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many fina…
Deep learning based numerical approximation algorithms for stochastic partial differential equations
Christian Beck, Sebastian Becker, Patrick Cheridito +2
In this article, we introduce a deep learning based approximation algorithm for SPDEs. Our approach employs neural networks to approximate the solutions of SPDEs along given realiz…
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations
Sebastian Becker, Ramon Braunwarth, Martin Hutzenthaler +2
One of the most challenging issues in applied mathematics is to develop and analyze algorithms which are able to approximately compute solutions of high-dimensional nonlinear parti…
Deep splitting method for parabolic PDEs
Christian Beck, Sebastian Becker, Patrick Cheridito +2
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequ…