P. Werner

most citedDeep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations

5 citations · 6 across the 3 of their papers we have counts for

collaborators

3 papers

math.FA2025

$H^{\infty}$ -calculus for the Dirichlet Laplacian on conical domains

Petru A. Cioica-Licht, Emiel Lorist, P. Tobias Werner

We establish boundedness of the $H^{\infty}$ -calculus for the Dirichlet Laplacian on conical domains in $R^{d}$ and corresponding wedges on $L^{p}$ -spaces with mixed weights. Th…

cs.LG2022★ 1 cited

The Ability of Image-Language Explainable Models to Resemble Domain Expertise

Petrus Werner, Anna Zapaishchykova, Ujjwal Ratan

Recent advances in vision and language (V+L) models have a promising impact in the healthcare field. However, such models struggle to explain how and why a particular decision was…

math.NA2022★ 5 cited

Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations

Petru A. Cioica-Licht, Martin Hutzenthaler, P. Tobias Werner

We prove that deep neural networks are capable of approximating solutions of semilinear Kolmogorov PDE in the case of gradient-independent, Lipschitz-continuous nonlinearities, whi…

H∞-calculus for the Dirichlet Laplacian on conical domains

The Ability of Image-Language Explainable Models to Resemble Domain Expertise

Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations

$H^{\infty}$ -calculus for the Dirichlet Laplacian on conical domains