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

1.8k citations

Showing 2015Show all

8 papers · 1 filter

astro-ph.IM2015★ 67 cited

An advanced leakage scheme for neutrino treatment in astrophysical simulations

Albino Perego, Ruben Cabezón, Roger Käppeli

We present an Advanced Spectral Leakage (ASL) scheme to model neutrinos in the context of core-collapse supernovae and compact binary mergers. Based on previous gray leakage scheme…

math.PR2015★ 17 cited

Weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise

Ladislas Jacobe de Naurois, Arnulf Jentzen, Timo Welti

Stochastic wave equations appear in several models for evolutionary processes subject to random forces, such as the motion of a strand of DNA in a liquid or heat flow around a ring…

math.CA2015★ 9 cited

Stability estimates for the regularized inversion of the truncated Hilbert transform

Rima Alaifari, Michel Defrise, Alexander Katsevich

In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection (DBP) method. Each 1D problem consis…

math.NA2015★ 30 cited

On stochastic differential equations with arbitrary slow convergence rates for strong approximation

Arnulf Jentzen, Thomas Müller-Gronbach, Larisa Yaroslavtseva

In the recent article [Hairer, M., Hutzenthaler, M., Jentzen, A., Loss of regularity for Kolmogorov equations, Ann. Probab. 43 (2015), no. 2, 468--527] it has been shown that there…

math.NA2015★ 99 cited

A Survey of Trefftz Methods for the Helmholtz Equation

Ralf Hiptmair, Andrea Moiola, Ilaria Perugia

Trefftz methods are finite element-type schemes whose test and trial functions are (locally) solutions of the targeted differential equation. They are particularly popular for time…

math.NA2015★ 99 cited

Trefftz discontinuous Galerkin methods on unstructured meshes for the wave equation

Andrea Moiola

We describe and analyse a space-time Trefftz discontinuous Galerkin method for the wave equation. The method is defined for unstructured meshes whose internal faces need not be ali…

math.PR2015★ 26 cited

Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities

Arnulf Jentzen, Primož Pušnik

In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipsch…

math.PR2015★ 38 cited

Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients

Arnulf Jentzen, Ryan Kurniawan

Strong convergence rates for time-discrete numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood i…