| Optimal approximation of piecewise smooth functions using deep ReLU neural networks P Petersen, F Voigtlaender Neural Networks 108, 296-330, 2018 | 414 | 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 | 263 | 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 | 167 | 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 | 153 | 2020 |
| Deep ReLU Networks and High-Order Finite Element Methods J Opschoor, P Petersen, C Schwab SAM Technical Report, 2019 | 120 | 2019 |
| Mathematical capabilities of chatgpt S Frieder, L Pinchetti, RR Griffiths, T Salvatori, T Lukasiewicz, ... arXiv preprint arXiv:2301.13867, 2023 | 119 | 2023 |
| The modern mathematics of deep learning J Berner, P Grohs, G Kutyniok, P Petersen arXiv preprint arXiv:2105.04026, 86-114, 2021 | 104 | 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 | 89 | 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 | 73 | 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 | 67 | 2021 |
| Classification of edges using compactly supported shearlets G Kutyniok, P Petersen Applied and Computational Harmonic Analysis 42 (2), 245-293, 2017 | 57 | 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 | 45 | 2021 |
| 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 | 25 | 2019 |
| 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 | 23 | 2023 |
| Neural network theory PC Petersen University of Vienna 535, 2020 | 21 | 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 | 21 | 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 | 15 | 2023 |
| Approximation in Lp(µ) with deep ReLU neural networks F Voigtlaender, P Petersen 2019 13th International conference on Sampling Theory and Applications …, 2019 | 13 | 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 | 10 | 2022 |
| Shearlet approximation of functions with discontinuous derivatives P Petersen Journal of Approximation Theory 207, 127-138, 2016 | 10 | 2016 |
Gitta KutyniokBavarian AI Chair for Mathematical Foundations of Artificial Intelligence, LMU MunichVerified email at math.lmu.de
