Journal articles

  1. Gitta Kutyniok, Philipp Petersen, Mones Raslan, and Reinhold Schneider, A Theoretical Analysis of Deep Neural Networks and Parametric PDEs , Constructive Approximation, in Press
  2. Philipp Petersen and Endre Süli, Gamma-convergence of a shearlet-based Ginzburg--Landau energy, Applied and Computational Harmonic Analysis, in Press
  3. 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, in Press
  4. Philipp Grohs, Gitta Kutyniok, Jackie Ma, Philipp Petersen, and Mones Raslan, Anisotropic multiscale systems on bounded domains, Advances in Computational Mathematics, in Press
  5. Joost Opschoor, Philipp Petersen, and Christoph Schwab, Deep ReLU Networks and High-Order Finite Element Methods, Analysis and Applications, in Press
  6. 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
  7. Philipp Petersen and Felix Voigtlaender, Equivalence of approximation by convolutional neural networks and fully-connected networks, Proceedings of the AMS, in Press
  8. 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
  9. 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
  10. Philipp Petersen and Mones Raslan, Approximation properties of shearlet frames for Sobolev Spaces, Advances in Computational Mathematics, in Press
  11. Philipp Petersen and Felix Voigtlaender, Optimal approximation of piecewise smooth functions using deep ReLU neural networks, Neural Networks, 108, 296--330, 2018.
  12. 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.
  13. 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
  14. Gitta Kutyniok and Philipp Petersen, Classification of edges using compactly supported shearlets, Applied and Computational Harmonic Analysis 42(2), 245--293, 2017
  15. Philipp Petersen, Shearlet approximation of functions with discontinuous derivatives, Journal of Approximation Theory 207, 127--138, 2016
  16. Jackie Ma and Philipp Petersen, Linear independence of compactly supported separable shearlet systems, Journal of Mathematical Analysis and Applications 428(1), 238--257, 2015

Conference Proceedings

  • Ingo Gühring, Gitta Kutyniok, Philipp Petersen, Error bounds for approximations with deep ReLU neural networks in Sobolev norms, Signal Processing with Adaptive Sparse Structured Representations (SPARS) Workshop 2019, Toulouse, France, 2019
  • Felix Voigtlaender, Philipp Petersen, Approximation in Lp(μ) with deep ReLU neural networks, Proc. of Intl.Conf. on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019
  • Philipp Petersen, Mones Raslan, Felix Voigtlaender, Unfavorable structural properties of the set of neural networks with fixed architecture, Proc. of Intl.Conf. on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019
  • Helmut Boelcskei, Philipp Grohs, Gitta Kutyniok, and Philipp Petersen, Memory-optimal neural network approximation, Proc. of SPIE (Wavelets and Sparsity XVII), San Diego, USA, 2017

Preprints


Monographs

  • Applications of Shearlet Frames for a Sparsity Promoting Regularization of the Inverse Scattering Problem
    Philipp Petersen, Master thesis
    Technische Universität Berlin, 2013
  • Nonnegative Completions of Block Operators
    Philipp Petersen, Bachelor thesis
    Technische Universität Berlin, 2011

Lecture notes