Publications
Harar P, Herrmann L, Grohs P, Haselbach D. FakET: Simulating Cryo-Electron Tomograms with Neural Style Transfer. 2023. Epub 2023 Apr 17. doi: 10.48550/ARXIV.2304.02011
Grohs P, Voigtländer F. Sobolev-type embeddings for neural network approximation spaces. 2 ed. 2023 Apr, p. 579-599. doi: 10.1007/s00365-022-09598-x
Liehr L, Grohs P. Non-uniqueness theory in sampled STFT phase retrieval. SIAM Journal on Mathematical Analysis. 2023 Mar 21. Epub 2023 Mar 21. doi: https://doi.org/10.48550/arXiv.2207.05628
Grohs P, Klotz A, Voigtlaender F. Phase Transitions in Rate Distortion Theory and Deep Learning. Foundations of Computational Mathematics. 2023 Feb;23(1):329-392. Epub 2021 Nov 16. doi: https://doi.org/10.1007/s10208-021-09546-4
Grohs P, Liehr L. Injectivity of Gabor phase retrieval from lattice measurements. Applied and Computational Harmonic Analysis. 2023 Jan;62:173-193. doi: https://arxiv.org/abs/2008.07238, 10.1016/j.acha.2022.09.001
Grohs P, Hornung F, Jentzen A, Zimmermann P. Space-time error estimates for deep neural network approximations for differential equations. Advances in Computational Mathematics. 2023;49:4. doi: 10.48550/arXiv.1908.03833, https://doi.org/10.1007/s10444-022-09970-2
Liehr L, Grohs P, Shafkulovska I. From completeness of discrete translates to phaseless sampling of the short-time Fourier transform. 2022 Nov 11. doi: 10.48550/arXiv.2211.05687
Abdeljawad A, Grohs P. Integral representations of shallow neural network with Rectified Power Unit activation function. Neural Networks. 2022 Nov;155:536 - 550. Epub 2022 Sep 14. doi: 10.1016/j.neunet.2022.09.005
Liehr L, Grohs P. Phaseless sampling on square-root lattices. 2022 Sep 22. doi: 10.48550/arXiv.2209.11127
Grohs P, Jentzen A, Salimova D. Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms. SN Partial Differential Equations and Applications. 2022 Aug;3(4):45. doi: https://doi.org/10.1007/s42985-021-00100-z
Grohs P, Herrmann L. Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions. IMA Journal of Numerical Analysis. 2022 Jul 22;42(3):2055-2082. drab031. Epub 2021 May 10. doi: 10.1093/imanum/drab031
Liehr L, Grohs P, Rathmair M. Multi-window STFT phase retrieval: lattice uniqueness. arXiv.org. 2022 Jul 21. doi: 10.48550/arXiv.2207.10620
Gonon L, Grohs P, Jentzen A, Kofler D, Siska D. Uniform error estimates for artificial neural network approximations for heat equations. IMA Journal of Numerical Analysis. 2022 Jul;42(3):1991-2054. drab027. Epub 2021 Aug 10. doi: 10.1093/imanum/drab027
Scherbela M, Reisenhofer R, Gerard L, Marquetand P, Grohs P. Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks. Nature Computational Science. 2022 May 19;2(5):331–341. doi: 10.1038/s43588-022-00228-x
Abdeljawad A, Grohs P. Approximations with deep neural networks in Sobolev time-space. Analysis and Applications. 2022 May 10;20(3):499 -541. doi: https://doi.org/10.1142/S0219530522500014
Liehr L, Grohs P. On foundational discretization barriers in STFT phase retrieval. Journal of Fourier Analysis and Applications. 2022 Apr;28:39. doi: 10.1007/s00041-022-09935-5
Bauer L, Hirsch F, Jones C, Hollander M, Grohs P, Anand A et al. Quantification of Kuramoto Coupling Between Intrinsic Brain Networks Applied to fMRI Data in Major Depressive Disorder. Frontiers in Computational Neuroscience. 2022 Mar 3;16:729556. doi: 10.3389/fncom.2022.729556
Schneckenreiter G, Herrmann L, Reisenhofer R, Popper N, Grohs P. Assessing the heterogeneity in the transmission of infectious diseases from time series of epidemiological data. medRxiv. 2022 Mar 1. doi: https://doi.org/10.1101/2022.02.21.22271241
Elbrächter D, Grohs P, Jentzen A, Schwab C. DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing. Constructive Approximation. 2022 Feb;55(1):3-71. Epub 2021 May 6. doi: 10.1007/s00365-021-09541-6
Berner J, Grohs P, Kutyniok G, Petersen PC. Die Moderne Mathematik des Tiefen Lernens. In Mitteilungen der DMV. 4 ed. Vol. 29. De Gruyter. 2022. p. 191-197. (Mitteilungen der Deutschen Mathematiker-Vereinigung). doi: https://doi.org/10.1515/dmvm-2021-0074