Journal articles

1. Hector Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, Philipp Petersen, Deep microlocal reconstruction for limited-angle tomography, Applied and Computational Harmonic Analysis, in Press.
2. Carlo Marcati, Joost A. A. Opschoor, Philipp C. Petersen, Christoph Schwab, Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities Foundations of Computational Mathematics, in Press
3. Moritz Geist, Philipp Petersen, Mones Raslan, Reinhold Schneider, Gitta Kutyniok, Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks Journal of Scientific Computing, in Press
4. Fabian Laakmann, Philipp Petersen, Efficient Approximation of Solutions of Parametric Linear Transport Equations by ReLU DNNs, Advances in Computational Mathematics, 47(11), 2021.
5. Gitta Kutyniok, Philipp Petersen, Mones Raslan, and Reinhold Schneider, A Theoretical Analysis of Deep Neural Networks and Parametric PDEs , Constructive Approximation, in Press
6. Philipp Petersen and Endre Süli, Gamma-convergence of a shearlet-based Ginzburg--Landau energy, Applied and Computational Harmonic Analysis, 49(3), 2020
7. Philipp Petersen, Felix Voigtlaender, and Mones Raslan, Topological properties of the set of functions generated by neural networks of fixed size, Foundations of Computational Mathematics, 21, 2021
8. Philipp Grohs, Gitta Kutyniok, Jackie Ma, Philipp Petersen, and Mones Raslan, Anisotropic multiscale systems on bounded domains, Advances in Computational Mathematics, 46(39), 2020
9. Joost Opschoor, Philipp Petersen, and Christoph Schwab, Deep ReLU Networks and High-Order Finite Element Methods, Analysis and Applications, 18(5), 2020
10. Hector Andrade-Loarca, Gitta Kutyniok, Ozan Öktem, and Philipp Petersen, Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks, SIAM Journal on Imaging Sciences, 12(4), 1936--1966, 2019
11. Philipp Petersen and Felix Voigtlaender, Equivalence of approximation by convolutional neural networks and fully-connected networks, Proceedings of the AMS, in Press
12. Ingo Gühring, Gitta Kutyniok, and Philipp Petersen, Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms , Analysis and Applications, in Press
13. Helmut Boelcskei, Philipp Grohs, Gitta Kutyniok, and Philipp Petersen, Optimal Approximation with Sparsely Connected Deep Neural Networks, SIAM Journal on Mathematics of Data Science, 1(1), 8--45, 2019
14. Philipp Petersen and Mones Raslan, Approximation properties of shearlet frames for Sobolev Spaces, Advances in Computational Mathematics, in Press
15. Philipp Petersen and Felix Voigtlaender, Optimal approximation of piecewise smooth functions using deep ReLU neural networks, Neural Networks, 108, 296--330, 2018.
16. Christian Lessig, Philipp Petersen, and Martin Schäfer, Bendlets: A Second-Order Shearlet Transform with Bent Elements, Applied and Computational Harmonic Analysis, 46(2), 384--399, 2019.
17. Gitta Kutyniok, Volker Mehrmann, and Philipp Petersen, Regularization and Numerical Solution of the Inverse Scattering Problem using Shearlet Frames, Journal of Inverse and Ill-Posed Problems, 25(3), 287--309, 2017
18. Gitta Kutyniok and Philipp Petersen, Classification of edges using compactly supported shearlets, Applied and Computational Harmonic Analysis 42(2), 245--293, 2017
19. Philipp Petersen, Shearlet approximation of functions with discontinuous derivatives, Journal of Approximation Theory 207, 127--138, 2016
20. Jackie Ma and Philipp Petersen, Linear independence of compactly supported separable shearlet systems, Journal of Mathematical Analysis and Applications 428(1), 238--257, 2015