135 citations · 234 across the 30 of their papers we have counts for
5 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…
Multilevel Picard approximation algorithm for semilinear partial integro-differential equations and its complexity analysis
Ariel Neufeld, Sizhou Wu
In this paper we introduce a multilevel Picard approximation algorithm for semilinear parabolic partial integro-differential equations (PIDEs). We prove that the numerical approxim…
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…
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…
Strong error analysis for stochastic gradient descent optimization algorithms
Arnulf Jentzen, Benno Kuckuck, Ariel Neufeld +1
Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of machine learning applications. In this article we perform a rigorous strong error analy…