Publications
Liehr L, Grohs P. Stable Gabor Phase Retrieval in Gaussian Shift-Invariant Spaces via Biorthogonality. Constructive Approximation. 2024 Feb;59(1):61-111. doi: 10.1007/s00365-023-09629-1
Scherbela M, Gerard L, Grohs P. Towards a transferable fermionic neural wavefunction for molecules. Nature Communications. 2024;15(1):120. doi: https://doi.org/10.1038/s41467-023-44216-9
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
Liehr L, Grohs P. Phaseless sampling on square-root lattices. Foundations of Computational Mathematics. 2023 Feb 8. doi: 10.1007/s10208-024-09640-3
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, VonWurstemberger P. A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. Memoirs of the American Mathematical Society. 2023;284(1410).
Berner J, Grohs P, Voigtlaender F. Learning ReLU networks to high uniform accuracy is intractable. 2023. Paper presented at The Eleventh International Conference on Learning Representations: ICLR 2023.
Liehr L, Grohs P, Rathmair M. Phase retrieval in Fock space and perturbation of Liouville sets. 2023.
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
Scherbela M, Gerard L, Grohs P. Variational Monte Carlo on a Budget - Fine-tuning pretrained Neural Wavefunctions. In Advances in Neural Information Processing Systems 36 (NeurIPS 2023). 2023
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