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 2013Show all

4 papers · 1 filter

math.NA2013★ 11 cited

Consistency and Stability of a Milstein-Galerkin Finite Element Scheme for Semilinear SPDE

Raphael Kruse

We present an abstract concept for the error analysis of numerical schemes for semilinear stochastic partial differential equations (SPDEs) and demonstrate its usefulness by provin…

math.PR2013★ 13 cited

Kolmogorov-Chentsov theorem and differentiability of random fields on manifolds

Roman Andreev, Annika Lang

A version of the Kolmogorov-Chentsov theorem on sample differentiability and Hölder continuity of random fields on domains of cone type is proved, and the result is generalized to…

math.NA2013★ 104 cited

Galerkin approximations for the stochastic Burgers equation

Dirk Blömker, Arnulf Jentzen

Existence and uniqueness for semilinear stochastic evolution equations with additive noise by means of finite dimensional Galerkin approximations is established and the convergence…

math-ph2013★ 24 cited

Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations

E. Weinan, Arnulf Jentzen, Hao Shen

This article analyzes well-definedness and regularity of renormalized powers of Ornstein-Uhlenbeck processes and uses this analysis to establish local existence, uniqueness and reg…