output
19992022
most citedSolving high-dimensional partial differential equations using deep learning

1.8k citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

collaborating institutions
Showing 2016 · math.NAShow all

4 papers · 2 filters

math.NA2016

Convergence rates of finite difference schemes for the linear advection and wave equation with rough coefficient

Franziska Weber

We prove convergence rates of explicit finite difference schemes for the linear advection and wave equation in one space dimension with Hölder continuous coefficient. The obtained…

math.NA2016★ 69 cited

Multilevel Picard iterations for solving smooth semilinear parabolic heat equations

Weinan E, Martin Hutzenthaler, Arnulf Jentzen +1

We introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time p…

math.NA2016★ 22 cited

Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions

Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen +2

We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process which is strongly Hölder continuous in ti…

math.NA2016

Analysis and Simulation on a Model for the Evolution of Tumors under the Influence of Nutrient and Drug Application

Konstantina Trivisa, Franziska Weber

We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with…