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 2014Show all

6 papers · 1 filter

math.NA2014★ 15 cited

Computation of measure-valued solutions for the incompressible Euler equations

Samuel Lanthaler, Siddhartha Mishra

We combine the spectral (viscosity) method and ensemble averaging to propose an algorithm that computes admissible measure valued solutions of the incompressible Euler equations. T…

math.NA2014★ 4 cited

Compressive sensing Petrov-Galerkin approximation of high-dimensional parametric operator equations

Holger Rauhut, Christoph Schwab

We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-paramet…

math.PR2014★ 34 cited

Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients

Daniel Conus, Arnulf Jentzen, Ryan Kurniawan

Strong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are…

math.NA2014

A Posteriori Error Estimation of hp-dG Finite Element Methods for Highly Indefinite Helmholtz Problems (extended version)

Stefan Sauter, Jakob Zech

In this paper, we will consider an -finite elements discretization of a highly indefinite Helmholtz problem by some dG formulation which is based on the ultra-weak variational…

math.AP2014★ 28 cited

Spectral properties of the Neumann-Poincaré operator and uniformity of estimates for the conductivity equation with complex coefficients

Hyeonbae Kang, Kyoungsun Kim, Hyundae Lee +2

We consider well-posedness of the boundary value problem in presence of an inclusion with complex conductivity . We first consider the transmission problem in and…

math.NA2014★ 116 cited

Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws

Ulrik S. Fjordholm, Roger Käppeli, Siddhartha Mishra +1

Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in \cite{CDL1,C…