Publications
Showing entries 21 - 40 out of 109
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: 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: 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. Mitteilungen der Deutschen Mathematiker-Vereinigung. 2022;29(4):191-197. doi: 10.1515/dmvm-2021-0074
Gerard L, Scherbela M, Marquetand P, Grohs P. Gold-standard solutions to the Schrödinger equation using deep learning: How much physics do we need?. 2022. Paper presented at Thirty-sixth Conference on Neural Information Processing Systems, New Orleans, United States.
Grohs P, Ibragimov S, Jentzen A, Koppensteiner S. Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality. Journal of Complexity. 2022. doi: 10.48550/arXiv.2103.04488
Grohs P, Rathmair M. Stable Gabor phase retrieval for multivariate functions. Journal of the European Mathematical Society. 2022;24(5):1593-1615. Epub 2021 Jul 19. doi: 10.4171/jems/1114
Grohs P, Kritzer P, Kunisch K, Ramlau R, Scherzer O. RICAM, the Johann Radon Institute for Computational and Applied Mathematics. EMS magazine. 2021 Dec;(122):46-51. doi: 10.4171/mag-37
Verdun CM, Fuchs T, Harár P, Elbrächter D, Fischer DS, Berner J et al. Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies. Frontiers in Public Health. 2021 Aug 18;9:1205. 583377. doi: 10.3389/fpubh.2021.583377
Elbrächter D, Perekrestenko D, Grohs P, Bölcskei H. Deep Neural Network Approximation Theory. IEEE TRANSACTIONS ON INFORMATION THEORY. 2021 May;67(5):2581-2623. 9363169. doi: 10.1109/TIT.2021.3062161
Alaifari R, Grohs P. Gabor Phase Retrieval is Severely Ill-Posed. Applied and Computational Harmonic Analysis. 2021 Jan;50:401-419. Epub 2019 Sept 22. doi: 10.1016/j.acha.2019.09.003
Grohs P, Kutyniok G, Ma J, Petersen PC, Raslan M. Anisotropic Multiscale Systems on Bounded Domains. Advances in Computational Mathematics. 2020 Apr 13;46:39. doi: 10.1007/s10444-020-09784-0
Grohs P. Analysis of edge and corner points using parabolic dictionaries. Applied and Computational Harmonic Analysis. 2020 Mar;48(2):655-681. doi: 10.1016/j.acha.2018.08.005
Berner J, Grohs P, Jentzen A. Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. SIAM Journal on Mathematics of Data Science. 2020;2(3):631-657. doi: 10.1137/19M125649X