153 citations · 899 across the 45 of their papers we have counts for
5 papers · 1 filter
Approximations with deep neural networks in Sobolev time-space
Ahmed Abdeljawad, Philipp Grohs
Solutions of evolution equation generally lies in certain Bochner-Sobolev spaces, in which the solution may has regularity and integrability properties for the time variable that c…
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning
Julius Berner, Markus Dablander, Philipp Grohs
We present a deep learning algorithm for the numerical solution of parametric families of high-dimensional linear Kolmogorov partial differential equations (PDEs). Our method is ba…
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions
Philipp Grohs, Lukas Herrmann
In recent work it has been established that deep neural networks are capable of approximating solutions to a large class of parabolic partial differential equations without incurri…
Phase Transitions in Rate Distortion Theory and Deep Learning
Philipp Grohs, Andreas Klotz, Felix Voigtlaender
Rate distortion theory is concerned with optimally encoding a given signal class using a budget of bits, as . We say that can be compres…
Injectivity of Gabor phase retrieval from lattice measurements
Philipp Grohs, Lukas Liehr
We establish novel uniqueness results for the Gabor phase retrieval problem: if denotes the Gabor transform then every $f \in…