153 citations · 899 across the 45 of their papers we have counts for
3 papers · 2 filters
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
Philipp Grohs, Fabian Hornung, Arnulf Jentzen +1
Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems ranging from image classification/image recogniti…
Solving the Kolmogorov PDE by means of deep learning
Christian Beck, Sebastian Becker, Philipp Grohs +2
Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations (PDEs) associated to them have been widely used in models from engineering, finance, and…
Projection-Based Finite Elements for Nonlinear Function Spaces
Philipp Grohs, Hanne Hardering, Oliver Sander +1
We introduce a novel type of approximation spaces for functions with values in a nonlinear manifold. The discrete functions are constructed by piecewise polynomial interpolation in…