Philipp Petersen

Publication Activity (10 Years)

Years Active: 2016-2024
Publications (10 Years): 24

Top Topics

Smooth Functions

Diffusion Equation

Top Venues

Adv. Comput. Math.

J. Approx. Theory

SIAM J. Math. Data Sci.

Publications

Philipp Petersen, Jakob Zech
Mathematical theory of deep learning. CoRR (2024)
Simon Frieder, Luca Pinchetti, Alexis Chevalier, Ryan-Rhys Griffiths, Tommaso Salvatori, Thomas Lukasiewicz, Philipp Petersen, Julius Berner
Mathematical Capabilities of ChatGPT. NeurIPS (2023)
Simon Frieder, Julius Berner, Philipp Petersen, Thomas Lukasiewicz
Large Language Models for Mathematicians. CoRR (2023)
Philipp Petersen, Mones Raslan, Felix Voigtländer
Topological Properties of the Set of Functions Generated by Neural Networks of Fixed Size. Found. Comput. Math. 21 (2) (2021)
Fabian Laakmann, Philipp Petersen
Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs. Adv. Comput. Math. 47 (1) (2021)
Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, Philipp Petersen
Deep Microlocal Reconstruction for Limited-Angle Tomography. CoRR (2021)
Julius Berner, Philipp Grohs, Gitta Kutyniok, Philipp Petersen
The Modern Mathematics of Deep Learning. CoRR (2021)
Philipp Petersen, Felix Voigtländer
Optimal learning of high-dimensional classification problems using deep neural networks. CoRR (2021)
Moritz Geist, Philipp Petersen, Mones Raslan, Reinhold Schneider, Gitta Kutyniok
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks. J. Sci. Comput. 88 (1) (2021)
Fabian Laakmann, Philipp Petersen
Efficient Approximation of Solutions of Parametric Linear Transport Equations by ReLU DNNs. CoRR (2020)
Philipp Grohs, Gitta Kutyniok, Jackie Ma, Philipp Petersen, Mones Raslan
Anisotropic multiscale systems on bounded domains. Adv. Comput. Math. 46 (2) (2020)
Moritz Geist, Philipp Petersen, Mones Raslan, Reinhold Schneider, Gitta Kutyniok
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks. CoRR (2020)
Felix Voigtländer, Philipp Petersen
(μ) with deep ReLU neural networks. CoRR (2019)
Ingo Gühring, Gitta Kutyniok, Philipp Petersen
Error bounds for approximations with deep ReLU neural networks in $W^{s, p}$ norms. CoRR (2019)
Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, Philipp Petersen
Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks. SIAM J. Imaging Sci. 12 (4) (2019)
Philipp Petersen, Mones Raslan
Approximation properties of hybrid shearlet-wavelet frames for Sobolev spaces. Adv. Comput. Math. 45 (3) (2019)
Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen
Optimal Approximation with Sparsely Connected Deep Neural Networks. SIAM J. Math. Data Sci. 1 (1) (2019)
Gitta Kutyniok, Philipp Petersen, Mones Raslan, Reinhold Schneider
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs. CoRR (2019)
Héctor Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, Philipp Petersen
Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks. CoRR (2019)
Philipp Petersen, Felix Voigtländer
Equivalence of approximation by convolutional neural networks and fully-connected networks. CoRR (2018)
Philipp Petersen, Felix Voigtländer
Optimal approximation of piecewise smooth functions using deep ReLU neural networks. Neural Networks 108 (2018)
Philipp Petersen, Felix Voigtländer
Optimal approximation of piecewise smooth functions using deep ReLU neural networks. CoRR (2017)
Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen
Optimal Approximation with Sparsely Connected Deep Neural Networks. CoRR (2017)
Philipp Petersen
Shearlet approximation of functions with discontinuous derivatives. J. Approx. Theory 207 (2016)