1 citations · 2 across the 7 of their papers we have counts for
12 papers
Deep Microlocal Reconstruction for Limited-Angle Tomography
Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem +1
We present a deep learning-based algorithm to jointly solve a reconstruction problem and a wavefront set extraction problem in tomographic imaging. The algorithm is based on a rece…
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks
Moritz Geist, Philipp Petersen, Mones Raslan +2
We perform a comprehensive numerical study of the effect of approximation-theoretical results for neural networks on practical learning problems in the context of numerical analysi…
Efficient Approximation of Solutions of Parametric Linear Transport Equations by ReLU DNNs
Fabian Laakmann, Philipp Petersen
We demonstrate that deep neural networks with the ReLU activation function can efficiently approximate the solutions of various types of parametric linear transport equations. For…
Approximation in with deep ReLU neural networks
Felix Voigtlaender, Philipp Petersen
We discuss the expressive power of neural networks which use the non-smooth ReLU activation function by analyzing the approximation theoretic properties…
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs
Gitta Kutyniok, Philipp Petersen, Mones Raslan +1
We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge…
Error bounds for approximations with deep ReLU neural networks in norms
Ingo Gühring, Gitta Kutyniok, Philipp Petersen
We analyze approximation rates of deep ReLU neural networks for Sobolev-regular functions with respect to weaker Sobolev norms. First, we construct, based on a calculus of ReLU net…