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
9 papers · 2 filters
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse
Partial differential equations (PDEs) are a fundamental tool in the modeling of many real world phenomena. In a number of such real world phenomena the PDEs under consideration con…
Uniform error estimates for artificial neural network approximations for heat equations
Lukas Gonon, Philipp Grohs, Arnulf Jentzen +2
Recently, artificial neural networks (ANNs) in conjunction with stochastic gradient descent optimization methods have been employed to approximately compute solutions of possibly r…
Full error analysis for the training of deep neural networks
Christan Beck, Arnulf Jentzen, Benno Kuckuck
Deep learning algorithms have been applied very successfully in recent years to a range of problems out of reach for classical solution paradigms. Nevertheless, there is no complet…
Statistical solutions of the incompressible Euler equations
Samuel Lanthaler, Siddhartha Mishra, Carlos Parés-Pulido
We propose and study the framework of dissipative statistical solutions for the incompressible Euler equations. Statistical solutions are time-parameterized probability measures on…
Deep neural network approximations for Monte Carlo algorithms
Philipp Grohs, Arnulf Jentzen, Diyora Salimova
Recently, it has been proposed in the literature to employ deep neural networks (DNNs) together with stochastic gradient descent methods to approximate solutions of PDEs. There are…
Convergence rates of monotone schemes for conservation laws with discontinuous flux
Jayesh Badwaik, Adrian Montgomery Ruf
We prove that a class of monotone finite volume schemes for scalar conservation laws with discontinuous flux converge at a rate of in , whenever the flux…
Elastic energy regularization for inverse obstacle scattering problems
Julian Eckhardt, Ralf Hiptmair, Thorsten Hohage +2
By introducing a shape manifold as a solution set to solve inverse obstacle scattering problems we allow the reconstruction of general, not necessarily star-shaped curves. The bend…
On the convergence of the spectral viscosity method for the two-dimensional incompressible Euler equations with rough initial data
Samuel Lanthaler, Siddhartha Mishra
We propose a spectral viscosity method to approximate the two-dimensional Euler equations with rough initial data and prove that the method converges to a weak solution for a large…
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse +1
Deep neural networks and other deep learning methods have very successfully been applied to the numerical approximation of high-dimensional nonlinear parabolic partial differential…