63 citations · 198 across the 8 of their papers we have counts for
9 papers
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation
Arnulf Jentzen, Timo Welti
In spite of the accomplishments of deep learning based algorithms in numerous applications and very broad corresponding research interest, at the moment there is still no rigorous…
Generalised multilevel Picard approximations
Michael B. Giles, Arnulf Jentzen, Timo Welti
It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). In particular, most of the numeri…
Solving high-dimensional optimal stopping problems using deep learning
Sebastian Becker, Patrick Cheridito, Arnulf Jentzen +1
Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional op…
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients
Arnulf Jentzen, Diyora Salimova, Timo Welti
In recent years deep artificial neural networks (DNNs) have been successfully employed in numerical simulations for a multitude of computational problems including, for example, ob…
Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations
Arnulf Jentzen, Diyora Salimova, Timo Welti
In this paper we propose and analyze explicit space-time discrete numerical approximations for additive space-time white noise driven stochastic partial differential equations (SPD…
Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations
Ladislas Jacobe de Naurois, Arnulf Jentzen, Timo Welti
Although for a number of semilinear stochastic wave equations existence and uniqueness results for corresponding solution processes are known from the literature, these solution pr…
On the differentiability of solutions of stochastic evolution equations with respect to their initial values
Adam Andersson, Arnulf Jentzen, Ryan Kurniawan +1
In this article we study the differentiability of solutions of parabolic semilinear stochastic evolution equations (SEEs) with respect to their initial values. We prove that if the…
From Modular to Distributed Open Architectures: A Unified Decision Framework
Babak Heydari, Mohsen Mosleh, Kia Dalili
This paper introduces a conceptual, yet quantifiable, architecture framework by extending the notion of system modularity in its broadest sense. Acknowledging that modularity is no…
Weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise
Ladislas Jacobe de Naurois, Arnulf Jentzen, Timo Welti
Stochastic wave equations appear in several models for evolutionary processes subject to random forces, such as the motion of a strand of DNA in a liquid or heat flow around a ring…