Philipp Petersen
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Optimal approximation of piecewise smooth functions using deep ReLU neural networks
P Petersen, F Voigtlaender
Neural Networks 108, 296-330, 2018
Optimal approximation with sparsely connected deep neural networks
H Bolcskei, P Grohs, G Kutyniok, P Petersen
SIAM Journal on Mathematics of Data Science 1 (1), 8-45, 2019
A theoretical analysis of deep neural networks and parametric PDEs
G Kutyniok, P Petersen, M Raslan, R Schneider
Constructive Approximation 55 (1), 73-125, 2022
Error bounds for approximations with deep ReLU neural networks in norms
I Gühring, G Kutyniok, P Petersen
Analysis and Applications 18 (05), 803-859, 2020
Mathematical capabilities of chatgpt
S Frieder, L Pinchetti, RR Griffiths, T Salvatori, T Lukasiewicz, ...
arXiv preprint arXiv:2301.13867, 2023
Deep ReLU Networks and High-Order Finite Element Methods
J Opschoor, P Petersen, C Schwab
SAM Technical Report, 2019
The modern mathematics of deep learning
J Berner, P Grohs, G Kutyniok, P Petersen
arXiv preprint arXiv:2105.04026, 86-114, 2021
Topological properties of the set of functions generated by neural networks of fixed size
P Petersen, M Raslan, F Voigtlaender
Foundations of computational mathematics 21, 375-444, 2021
Equivalence of approximation by convolutional neural networks and fully-connected networks
P Petersen, F Voigtlaender
Proceedings of the American Mathematical Society 148 (4), 1567-1581, 2020
Numerical solution of the parametric diffusion equation by deep neural networks
M Geist, P Petersen, M Raslan, R Schneider, G Kutyniok
Journal of Scientific Computing 88 (1), 22, 2021
Classification of edges using compactly supported shearlets
G Kutyniok, P Petersen
Applied and Computational Harmonic Analysis 42 (2), 245-293, 2017
Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs
F Laakmann, P Petersen
Advances in Computational Mathematics 47, 1-32, 2021
Neural network approximation and estimation of classifiers with classification boundary in a Barron class
A Caragea, P Petersen, F Voigtlaender
The Annals of Applied Probability 33 (4), 3039-3079, 2023
Bendlets: A second-order shearlet transform with bent elements
C Lessig, P Petersen, M Schäfer
Applied and Computational Harmonic Analysis 46 (2), 384-399, 2019
Neural network theory
PC Petersen
University of Vienna 535, 2020
Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks
H Andrade-Loarca, G Kutyniok, O Öktem, P Petersen
arXiv preprint arXiv:1901.01388, 2019
Exponential relu neural network approximation rates for point and edge singularities
C Marcati, JAA Opschoor, PC Petersen, C Schwab
Foundations of Computational Mathematics 23 (3), 1043-1127, 2023
Approximation in Lp(µ) with deep ReLU neural networks
F Voigtlaender, P Petersen
2019 13th International conference on Sampling Theory and Applications …, 2019
Deep microlocal reconstruction for limited-angle tomography
H Andrade-Loarca, G Kutyniok, O Öktem, P Petersen
Applied and Computational Harmonic Analysis 59, 155-197, 2022
Shearlet approximation of functions with discontinuous derivatives
P Petersen
Journal of Approximation Theory 207, 127-138, 2016
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