1.8k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- ETH ZurichCH99 papers
- University of MünsterDE18 papers
- University of PaviaIT9 papers
- University of ViennaAT9 papers
- University of Duisburg-EssenDE7 papers
- Chinese University of Hong Kong, ShenzhenCN6 papers
- Shenzhen Research Institute of Big DataCN6 papers
- University of Maryland, College ParkUS6 papers
- Princeton UniversityUS5 papers
- TU WienAT5 papers
- Austrian Academy of SciencesAT4 papers
- Chalmers University of TechnologySE4 papers
10 papers · 1 filter
Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions
Arnulf Jentzen, Felix Lindner, Primož Pušnik
In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform Hölder continuity in time, and strong convergence rates for a…
Low-rank Riemannian eigensolver for high-dimensional Hamiltonians
Maxim Rakhuba, Alexander Novikov, Ivan Oseledets
Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can b…
Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations
Sebastian Becker, Benjamin Gess, Arnulf Jentzen +1
Optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise are obtained. In particul…
On the Alekseev-Gröbner formula in Banach spaces
Arnulf Jentzen, Felix Lindner, Primož Pušnik
The Alekseev-Gröbner formula is a well known tool in numerical analysis for describing the effect that a perturbation of an ordinary differential equation (ODE) has on its solution…
Formal Solutions for Polarized Radiative Transfer. IV. Numerical Performances in Practical Problems
Gioele Janett, Oskar Steiner, Luca Belluzzi
The numerical computation of reliable and accurate Stokes profiles is of great relevance in solar physics. In the synthesis process, many actors play a relevant role: among them th…
DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing
Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen +1
We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReL…
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
Philipp Grohs, Fabian Hornung, Arnulf Jentzen +1
Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems ranging from image classification/image recogniti…
Solving the Kolmogorov PDE by means of deep learning
Christian Beck, Sebastian Becker, Philipp Grohs +2
Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations (PDEs) associated to them have been widely used in models from engineering, finance, and…
von Neumann Stability Analysis of Globally Constraint-Preserving DGTD and PNPM Schemes for the Maxwell Equations using Multidimensional Riemann Solvers
Dinshaw S. Balsara, Roger Kappeli
The time-dependent equations of computational electrodynamics (CED) are evolved consistent with the divergence constraints. As a result, there has been a recent effort to design fi…
Formal solutions for polarized radiative transfer. III. Stiffness and instability
Gioele Janett, Alberto Paganini
Efficient numerical approximation of the polarized radiative transfer equation is challenging because this system of ordinary differential equations exhibits stiff behavior, which…