Publications
Non-uniqueness theory in sampled STFT phase retrieval. / Liehr, Lukas; Grohs, Philipp.
In: SIAM Journal on Mathematical Analysis, 21.03.2023.Publication: Contribution to journal › Article › peer-review
Phase Transitions in Rate Distortion Theory and Deep Learning. / Grohs, Philipp; Klotz, Andreas; Voigtlaender, Felix (Corresponding author).
In: Foundations of Computational Mathematics, Vol. 23, No. 1, 02.2023, p. 329-392.Publication: Contribution to journal › Article › peer-review
Injectivity of Gabor phase retrieval from lattice measurements. / Grohs, Philipp; Liehr, Lukas (Corresponding author).
In: Applied and Computational Harmonic Analysis, Vol. 62, 01.2023, p. 173-193.Publication: Contribution to journal › Article › peer-review
Space-time error estimates for deep neural network approximations for differential equations. / Grohs, Philipp; Hornung, Fabian ; Jentzen, Arnulf; Zimmermann, Philipp (Corresponding author).
In: Advances in Computational Mathematics, Vol. 49, 4, 2023.Publication: Contribution to journal › Article › peer-review
From completeness of discrete translates to phaseless sampling of the short-time Fourier transform. / Liehr, Lukas; Grohs, Philipp; Shafkulovska, Irina.
2022.Publication: Working paper › Preprint
Integral representations of shallow neural network with Rectified Power Unit activation function. / Abdeljawad, Ahmed (Corresponding author); Grohs, Philipp.
In: Neural Networks, Vol. 155, 11.2022, p. 536 - 550.Publication: Contribution to journal › Article › peer-review
Phaseless sampling on square-root lattices. / Liehr, Lukas; Grohs, Philipp.
2022.Publication: Working paper › Preprint
Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms. / Grohs, Philipp; Jentzen, Arnulf (Corresponding author); Salimova , Diyora .
In: SN Partial Differential Equations and Applications, Vol. 3, No. 4, 45, 08.2022.Publication: Contribution to journal › Article › peer-review
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions. / Grohs, Philipp; Herrmann, Lukas (Corresponding author).
In: IMA Journal of Numerical Analysis, Vol. 42, No. 3, drab031, 22.07.2022, p. 2055-2082.Publication: Contribution to journal › Article › peer-review
Multi-window STFT phase retrieval: lattice uniqueness. / Liehr, Lukas; Grohs, Philipp; Rathmair, Martin.
arXiv.org, 2022.Publication: Working paper › Preprint
Uniform error estimates for artificial neural network approximations for heat equations. / Gonon, Lukas; Grohs, Philipp; Jentzen, Arnulf; Kofler, David; Siska, David .
In: IMA Journal of Numerical Analysis, Vol. 42, No. 3, drab027, 07.2022, p. 1991-2054.Publication: Contribution to journal › Article › peer-review
Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks. / Scherbela, Michael; Reisenhofer, Rafael (Corresponding author); Gerard, Leon; Marquetand, Philipp; Grohs, Philipp.
In: Nature Computational Science, Vol. 2, No. 5, 19.05.2022, p. 331–341.Publication: Contribution to journal › Article › peer-review
Approximations with deep neural networks in Sobolev time-space. / Abdeljawad, Ahmed (Corresponding author); Grohs, Philipp.
In: Analysis and Applications, Vol. 20, No. 3, 10.05.2022, p. 499 -541.Publication: Contribution to journal › Article › peer-review
On foundational discretization barriers in STFT phase retrieval. / Liehr, Lukas; Grohs, Philipp.
In: Journal of Fourier Analysis and Applications, Vol. 28, 39, 04.2022.Publication: Contribution to journal › Article › peer-review
Quantification of Kuramoto Coupling Between Intrinsic Brain Networks Applied to fMRI Data in Major Depressive Disorder. / Bauer, Lena; Hirsch, Fabian ; Jones, Corey; Hollander, Matthew; Grohs, Philipp; Anand, Amit ; Plant, Claudia; Wohlschläger, Afra (Corresponding author).
In: Frontiers in Computational Neuroscience, Vol. 16, 729556, 03.03.2022.Publication: Contribution to journal › Article › peer-review
DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing. / Elbrächter, Dennis (Corresponding author); Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph.
In: Constructive Approximation, Vol. 55, No. 1, 02.2022, p. 3-71.Publication: Contribution to journal › Article › peer-review
Die Moderne Mathematik des Tiefen Lernens. / Berner, Julius; Grohs, Philipp; Kutyniok, Gitta; Petersen, Philipp Christian.
Mitteilungen der DMV. Vol. 29 4. ed. De Gruyter, 2022. p. 191-197 (Mitteilungen der Deutschen Mathematiker-Vereinigung).Publication: Contribution to book › Chapter › peer-review
Gold-standard solutions to the Schrödinger equation using deep learning: How much physics do we need? / Gerard, Leon; Scherbela, Michael; Marquetand, Philipp; Grohs, Philipp.
2022. Paper presented at Thirty-sixth Conference on Neural Information Processing Systems, New Orleans, United States.Publication: Contribution to conference › Paper › peer-review
Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality. / Grohs, Philipp; Ibragimov, Shokhrukh ; Jentzen, Arnulf; Koppensteiner, Sarah.
In: Journal of Complexity, 2022.Publication: Contribution to journal › Article › peer-review
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces. / Grohs, Philipp; Voigtlaender, Felix.
2022.Publication: Working paper