Optimal approximation of piecewise smooth functions using deep ReLU neural networks P Petersen, F Voigtlaender
Neural Networks 108, 296-330, 2018
560 2018 Mathematical capabilities of chatgpt S Frieder, L Pinchetti, RR Griffiths, T Salvatori, T Lukasiewicz, P Petersen, ...
Advances in neural information processing systems 36, 2024
517 2024 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
313 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
234 2022 Error bounds for approximations with deep ReLU neural networks in I Gühring, G Kutyniok, P Petersen
Analysis and Applications 18 (05), 803-859, 2020
216 2020 The modern mathematics of deep learning J Berner, P Grohs, G Kutyniok, P Petersen
arXiv preprint arXiv:2105.04026 78, 2021
210 2021 Deep ReLU Networks and High-Order Finite Element Methods J Opschoor, P Petersen, C Schwab
SAM Technical Report, 2019
155 2019 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
118 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
100 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
96 2021 Classification of edges using compactly supported shearlets G Kutyniok, P Petersen
Applied and Computational Harmonic Analysis 42 (2), 245-293, 2017
64 2017 Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs F Laakmann, P Petersen
Advances in Computational Mathematics 47 (1), 11, 2021
58 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
47 2023 Mathematical capabilities of ChatGPT. arXiv S Frieder, L Pinchetti, RR Griffiths, T Salvatori, T Lukasiewicz, ...
arXiv preprint arXiv:2301.13867, 2023
37 2023 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
33 2023 Neural network theory PC Petersen
University of Vienna 535, 2020
33 2020 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
29 2019 Mathematical capabilities of chatgpt. arXiv 2023 S Frieder, L Pinchetti, RR Griffiths, T Salvatori, T Lukasiewicz, ...
arXiv preprint arXiv:2301.13867, 0
29 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
22 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
17 2022 
Gitta KutyniokBavarian AI Chair for Mathematical Foundations of Artificial Intelligence, LMU MunichBestätigte E-Mail-Adresse bei math.lmu.de
