Publications


Showing entries 1 - 20 out of 122

Non-uniqueness theory in sampled STFT phase retrieval. / Liehr, Lukas; Grohs, Philipp.

In: SIAM Journal on Mathematical Analysis, 21.03.2023.

Publication: Contribution to journalArticlepeer-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 journalArticlepeer-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 journalArticlepeer-review


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 journalArticlepeer-review


Phaseless sampling on square-root lattices. / Liehr, Lukas; Grohs, Philipp.

2022.

Publication: Working paperPreprint


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 journalArticlepeer-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 journalArticlepeer-review


Multi-window STFT phase retrieval: lattice uniqueness. / Liehr, Lukas; Grohs, Philipp; Rathmair, Martin.

arXiv.org, 2022.

Publication: Working paperPreprint


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 journalArticlepeer-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 journalArticlepeer-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 journalArticlepeer-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 journalArticlepeer-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 journalArticlepeer-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 journalArticlepeer-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 bookChapterpeer-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 conferencePaperpeer-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 journalArticlepeer-review


Showing entries 1 - 20 out of 122