47 citations · 105 across the 26 of their papers we have counts for
14 papers · 1 filter
Error analysis for the deep Kolmogorov method
Iulian Cîmpean, Thang Do, Lukas Gonon +2
The deep Kolmogorov method is a simple and popular deep learning based method for approximating solutions of partial differential equations (PDEs) of the Kolmogorov type. In this w…
A brief review of the Deep BSDE method for solving high-dimensional partial differential equations
Jiequn Han, Arnulf Jentzen, Weinan E
High-dimensional partial differential equations (PDEs) pose significant challenges for numerical computation due to the curse of dimensionality, which limits the applicability of t…
An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning
Lukas Gonon, Arnulf Jentzen, Benno Kuckuck +3
The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of meth…
Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions
Victor Boussange, Sebastian Becker, Arnulf Jentzen +2
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications…
Strong -error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations
Martin Hutzenthaler, Arnulf Jentzen, Benno Kuckuck +1
Full-history recursive multilevel Picard (MLP) approximation schemes have been shown to overcome the curse of dimensionality in the numerical approximation of high-dimensional semi…
Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse +1
Backward stochastic differential equations (BSDEs) belong nowadays to the most frequently studied equations in stochastic analysis and computational stochastics. BSDEs in applicati…