Peer Reviewed Journal Publication

  • Approximation Rates in Fréchet Metrics: Barron Spaces, Paley-Wiener Spaces, and Fourier Multipliers. / Abdeljawad, Ahmed; Dittrich, Thomas.
    in: Neural Computation, 01.12.2025, S. 1-33.
    DOIWebsiteRISENWBIB
  • Uniform approximation with quadratic neural networks. / Abdeljawad, Ahmed.
    in: Neural Networks, Jahrgang 192, 107742, 12.2025.
    DOIRISENWBIB
  • Transferable neural wavefunctions for solids. / Gerard, L.; Scherbela, M.; Sutterud, H. et al.
    in: Nature Computational Science, 22.10.2025.
    DOIRISENWBIB
  • From completeness of discrete translates to phaseless sampling of the short-time Fourier transform. / Grohs, Philipp; Liehr, Lukas; Shafkulovska, Irina.
    in: Advances in Computational Mathematics, Jahrgang 51, Nr. 3, 28, 13.06.2025.
    DOIRISENWBIB
  • FakET: Simulating cryo-electron tomograms with neural style transfer. / Harar, Pavol; Herrmann, Lukas; Grohs, Philipp et al.
    in: Structure, Jahrgang 33, Nr. 4, 03.04.2025, S. 820-827.
    DOIRISENWBIB
  • Phaseless Sampling on Square-Root Lattices. / Grohs, Philipp; Liehr, Lukas.
    in: Foundations of Computational Mathematics, Jahrgang 25, Nr. 2, 04.2025, S. 351-374.
    DOIRISENWBIB
  • Multi-window STFT phase retrieval: Lattice uniqueness. / Grohs, Philipp; Liehr, Lukas; Rathmair, Martin.
    in: Journal of Functional Analysis, Jahrgang 288, Nr. 3, 01.02.2025, S. ARTN 110733.
    DOIRISENWBIB
  • Phase retrieval in Fock space and perturbation of Liouville sets. / Grohs, Philipp; Liehr, Lukas; Rathmair, Martin.
    in: Revista Matematica Iberoamericana, Jahrgang 41, Nr. 3, 2025, S. 969-1008.
    DOIRISENWBIB
  • Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction. / Harbrecht, Helmut; Herrmann, Lukas; Kirchner, Kristin et al.
    in: Advances in Computational Mathematics, Jahrgang 50, Nr. 5, 15.10.2024, S. ARTN 101.
    DOIRISENWBIB
  • Neural and spectral operator surrogates: unified construction and expression rate bounds. / Herrmann, Lukas; Schwab, Christoph; Zech, Jakob.
    in: Advances in Computational Mathematics, Jahrgang 50, Nr. 4, 15.08.2024, S. ARTN 72.
    DOIRISENWBIB
  • Deep learning variational Monte Carlo for solving the electronic Schrödinger equation. / Gerard, Leon; Grohs, Philipp; Scherbela, Michael.
    in: Handbook of Numerical Analysis, Jahrgang 25, 30.06.2024, S. 231-292.
    DOIRISENWBIB
  • Sampling Complexity of Deep Approximation Spaces. / Abdeljawad, Ahmed; Grohs, Philipp.
    in: Analysis and Applications, Jahrgang 23, Nr. 01, 31.05.2024, S. 1-30.
    DOIWebsiteDownloadRISENWBIB
  • Towards a transferable fermionic neural wavefunction for molecules. / Scherbela, Michael; Gerard, Leon; Grohs, Philipp.
    in: Nature Communications, Jahrgang 15, Nr. 1, 02.01.2024, S. ARTN 120.
    DOIRISENWBIB
  • The fast reduced QMC matrix-vector product. / Dick, J.; Ebert, A.; Herrmann, L. et al.
    in: Journal of Computational and Applied Mathematics, Jahrgang 440, 07.11.2023, S. 115642.
    RISENWBIB
  • Stable Gabor Phase Retrieval in Gaussian Shift-Invariant Spaces via Biorthogonality. / Grohs, Philipp; Liehr, Lukas.
    in: Constructive Approximation, 04.10.2023.
    DOIRISENWBIB
  • 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 et al.
    in: Journal of Complexity, Jahrgang 77, 15.08.2023, S. ARTN 101746.
    DOIRISENWBIB
  • Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces. / Grohs, Philipp; Voigtlaender, Felix.
    in: Foundations of Computational Mathematics, 12.07.2023.
    DOIRISENWBIB
  • NON-UNIQUENESS THEORY IN SAMPLED STFT PHASE RETRIEVAL. / Grohs, Philipp; Liehr, Lukas.
    in: SIAM Journal on Mathematical Analysis, Jahrgang 55, Nr. 5, 15.06.2023, S. 4695-4726.
    DOIRISENWBIB
  • Assessing the heterogeneity in the transmission of infectious diseases from time series of epidemiological data. / Schneckenreither, Guenter; Herrmann, Lukas; Reisenhofer, Rafael et al.
    in: PLoS ONE, Jahrgang 18, Nr. 5, 15.05.2023.
    DOIRISENWBIB
  • A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations. / Grohs, Philipp; Hornung, Fabian; Jentzen, Arnulf et al.
    in: Memoirs of the American Mathematical Society, Jahrgang 284, Nr. 1410, 15.04.2023, S. 1-106.
    DOIRISENWBIB
  • Sobolev-Type Embeddings for Neural Network Approximation Spaces. / Grohs, Philipp; Voigtlaender, Felix.
    in: Constructive Approximation, 05.03.2023.
    DOIRISENWBIB
  • Analysis of rhc for stabilization of nonautonomous parabolic equations under uncertainty. / Azmi, Behzad; Kunisch, Karl K.; Herrmann, Lukas.
    in: SIAM Journal on Control and Optimization, Jahrgang 62, Nr. 1, 01.02.2023, S. 220-242.
    RISENWBIB
  • Injectivity of Gabor phase retrieval from lattice measurements. / Grohs, Philipp; Liehr, Lukas.
    in: Applied and Computational Harmonic Analysis, Jahrgang 62, 15.01.2023, S. 173-193.
    DOIRISENWBIB
  • Integral representations of shallow neural network with rectified power unit activation function. / Abdeljawad, Ahmed; Grohs, Philipp.
    in: Neural Networks, Jahrgang 155, 15.11.2022, S. 536-550.
    DOIRISENWBIB
  • Stable Gabor phase retrieval for multivariate functions. / Grohs, Philipp; Rathmair, Martin.
    in: Journal of the European Mathematical Society, Jahrgang 24, Nr. 5, 15.06.2022, S. 1593-1615.
    DOIRISENWBIB
  • Approximations with deep neural networks in Sobolev time-space. / Abdeljawad, Ahmed; Grohs, Philipp.
    in: Analysis and Applications, Jahrgang 20, Nr. 03, 15.05.2022, S. 499-541.
    DOIRISENWBIB
  • Solving the electronic Schrodinger equation for multiple nuclear geometries with weight-sharing deep neural networks. / Scherbela, Michael; Reisenhofer, Rafael; Gerard, Leon et al.
    in: Nature Computational Science, Jahrgang 2, Nr. 5, 15.05.2022, S. 331-341.
    DOIRISENWBIB
  • On Foundational Discretization Barriers in STFT Phase Retrieval. / Grohs, Philipp; Liehr, Lukas.
    in: Journal of Fourier Analysis and Applications, Jahrgang 28, Nr. 2, 15.04.2022, S. ARTN 39.
    DOIRISENWBIB
  • Constructive deep ReLU neural network approximation. / Herrmann, Lukas; Joost, A; Opschoor, A. et al.
    in: Journal of Scientific Computing, Nr. 90, 06.01.2022, S. Article number: 75.
    DOIRISENWBIB
  • Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies. / Verdun, Claudio M.; Fuchs, Tim; Harar, Pavol et al.
    in: Frontiers in Public Health, Jahrgang 9, 18.08.2021, S. ARTN 583377.
    DOIRISENWBIB
  • Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions. / Grohs, P.; Herrmann, L.
    in: IMA Journal of Numerical Analysis, Jahrgang tba, Nr. tba, 10.05.2021, S. tba.
    DOIRISENWBIB
  • DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing. / Elbraechter, Dennis; Grohs, Philipp; Jentzen, Arnulf et al.
    in: Constructive Approximation, 06.05.2021.
    DOIRISENWBIB
  • Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems. / Herrmann, L.; Keller, M.; Schwab, C.
    in: Mathematics of Computation, Jahrgang 90, Nr. 330, 10.03.2021, S. 1831-1860.
    DOIDownloadRISENWBIB
  • Deep Neural Network Expression of Posterior Expectations in Bayesian PDE Inversion. / Herrmann, L; Schwab, C; Zech, J.
    in: Inverse Problems, Jahrgang 36, Nr. 12, 03.12.2020, S. 125011.
    DOIDownloadRISENWBIB
  • Bilinear Pseudo-differential Operators with Gevrey-Hormander Symbols. / Abdeljawad, Ahmed; Coriasco, Sandro; Teofanov, Nenad.
    in: Mediterranean Journal of Mathematics, Jahrgang 17, Nr. 4, 27.06.2020, S. ARTN 120.
    DOIRISENWBIB
  • Characterizations of a class of Pilipovic spaces by powers of harmonic oscillator. / Abdeljawad, Ahmed; Fernandez, Carmen; Galbis, Antonio et al.
    in: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, Jahrgang 114, Nr. 3, 14.05.2020, S. ARTN 131.
    DOIRISENWBIB
  • Deterministic and stochastic Cauchy problems for a class of weakly hyperbolic operators on R-n. / Abdeljawad, Ahmed; Ascanelli, Alessia; Coriasco, Sandro.
    in: Monatshefte fur Mathematik, 21.02.2020.
    DOIRISENWBIB
  • Approximation Rates in Fréchet Metrics: Barron Spaces, Paley-Wiener Spaces, and Fourier Multipliers. / Abdeljawad, Ahmed; Dittrich, Thomas.
    in: Neural Computation, 01.12.2025, S. 1-33.
    DOIWebsiteRISENWBIB
  • Uniform approximation with quadratic neural networks. / Abdeljawad, Ahmed.
    in: Neural Networks, Jahrgang 192, 107742, 12.2025.
    DOIRISENWBIB
  • Transferable neural wavefunctions for solids. / Gerard, L.; Scherbela, M.; Sutterud, H. et al.
    in: Nature Computational Science, 22.10.2025.
    DOIRISENWBIB
  • From completeness of discrete translates to phaseless sampling of the short-time Fourier transform. / Grohs, Philipp; Liehr, Lukas; Shafkulovska, Irina.
    in: Advances in Computational Mathematics, Jahrgang 51, Nr. 3, 28, 13.06.2025.
    DOIRISENWBIB
  • FakET: Simulating cryo-electron tomograms with neural style transfer. / Harar, Pavol; Herrmann, Lukas; Grohs, Philipp et al.
    in: Structure, Jahrgang 33, Nr. 4, 03.04.2025, S. 820-827.
    DOIRISENWBIB
  • Phaseless Sampling on Square-Root Lattices. / Grohs, Philipp; Liehr, Lukas.
    in: Foundations of Computational Mathematics, Jahrgang 25, Nr. 2, 04.2025, S. 351-374.
    DOIRISENWBIB
  • Multi-window STFT phase retrieval: Lattice uniqueness. / Grohs, Philipp; Liehr, Lukas; Rathmair, Martin.
    in: Journal of Functional Analysis, Jahrgang 288, Nr. 3, 01.02.2025, S. ARTN 110733.
    DOIRISENWBIB
  • Phase retrieval in Fock space and perturbation of Liouville sets. / Grohs, Philipp; Liehr, Lukas; Rathmair, Martin.
    in: Revista Matematica Iberoamericana, Jahrgang 41, Nr. 3, 2025, S. 969-1008.
    DOIRISENWBIB
  • Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction. / Harbrecht, Helmut; Herrmann, Lukas; Kirchner, Kristin et al.
    in: Advances in Computational Mathematics, Jahrgang 50, Nr. 5, 15.10.2024, S. ARTN 101.
    DOIRISENWBIB
  • Neural and spectral operator surrogates: unified construction and expression rate bounds. / Herrmann, Lukas; Schwab, Christoph; Zech, Jakob.
    in: Advances in Computational Mathematics, Jahrgang 50, Nr. 4, 15.08.2024, S. ARTN 72.
    DOIRISENWBIB
  • Deep learning variational Monte Carlo for solving the electronic Schrödinger equation. / Gerard, Leon; Grohs, Philipp; Scherbela, Michael.
    in: Handbook of Numerical Analysis, Jahrgang 25, 30.06.2024, S. 231-292.
    DOIRISENWBIB
  • Sampling Complexity of Deep Approximation Spaces. / Abdeljawad, Ahmed; Grohs, Philipp.
    in: Analysis and Applications, Jahrgang 23, Nr. 01, 31.05.2024, S. 1-30.
    DOIWebsiteDownloadRISENWBIB
  • Towards a transferable fermionic neural wavefunction for molecules. / Scherbela, Michael; Gerard, Leon; Grohs, Philipp.
    in: Nature Communications, Jahrgang 15, Nr. 1, 02.01.2024, S. ARTN 120.
    DOIRISENWBIB
  • The fast reduced QMC matrix-vector product. / Dick, J.; Ebert, A.; Herrmann, L. et al.
    in: Journal of Computational and Applied Mathematics, Jahrgang 440, 07.11.2023, S. 115642.
    RISENWBIB
  • Stable Gabor Phase Retrieval in Gaussian Shift-Invariant Spaces via Biorthogonality. / Grohs, Philipp; Liehr, Lukas.
    in: Constructive Approximation, 04.10.2023.
    DOIRISENWBIB
  • 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 et al.
    in: Journal of Complexity, Jahrgang 77, 15.08.2023, S. ARTN 101746.
    DOIRISENWBIB
  • Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces. / Grohs, Philipp; Voigtlaender, Felix.
    in: Foundations of Computational Mathematics, 12.07.2023.
    DOIRISENWBIB
  • NON-UNIQUENESS THEORY IN SAMPLED STFT PHASE RETRIEVAL. / Grohs, Philipp; Liehr, Lukas.
    in: SIAM Journal on Mathematical Analysis, Jahrgang 55, Nr. 5, 15.06.2023, S. 4695-4726.
    DOIRISENWBIB
  • Assessing the heterogeneity in the transmission of infectious diseases from time series of epidemiological data. / Schneckenreither, Guenter; Herrmann, Lukas; Reisenhofer, Rafael et al.
    in: PLoS ONE, Jahrgang 18, Nr. 5, 15.05.2023.
    DOIRISENWBIB
  • A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations. / Grohs, Philipp; Hornung, Fabian; Jentzen, Arnulf et al.
    in: Memoirs of the American Mathematical Society, Jahrgang 284, Nr. 1410, 15.04.2023, S. 1-106.
    DOIRISENWBIB
  • Sobolev-Type Embeddings for Neural Network Approximation Spaces. / Grohs, Philipp; Voigtlaender, Felix.
    in: Constructive Approximation, 05.03.2023.
    DOIRISENWBIB
  • Analysis of rhc for stabilization of nonautonomous parabolic equations under uncertainty. / Azmi, Behzad; Kunisch, Karl K.; Herrmann, Lukas.
    in: SIAM Journal on Control and Optimization, Jahrgang 62, Nr. 1, 01.02.2023, S. 220-242.
    RISENWBIB
  • Injectivity of Gabor phase retrieval from lattice measurements. / Grohs, Philipp; Liehr, Lukas.
    in: Applied and Computational Harmonic Analysis, Jahrgang 62, 15.01.2023, S. 173-193.
    DOIRISENWBIB
  • Integral representations of shallow neural network with rectified power unit activation function. / Abdeljawad, Ahmed; Grohs, Philipp.
    in: Neural Networks, Jahrgang 155, 15.11.2022, S. 536-550.
    DOIRISENWBIB
  • Stable Gabor phase retrieval for multivariate functions. / Grohs, Philipp; Rathmair, Martin.
    in: Journal of the European Mathematical Society, Jahrgang 24, Nr. 5, 15.06.2022, S. 1593-1615.
    DOIRISENWBIB
  • Approximations with deep neural networks in Sobolev time-space. / Abdeljawad, Ahmed; Grohs, Philipp.
    in: Analysis and Applications, Jahrgang 20, Nr. 03, 15.05.2022, S. 499-541.
    DOIRISENWBIB
  • Solving the electronic Schrodinger equation for multiple nuclear geometries with weight-sharing deep neural networks. / Scherbela, Michael; Reisenhofer, Rafael; Gerard, Leon et al.
    in: Nature Computational Science, Jahrgang 2, Nr. 5, 15.05.2022, S. 331-341.
    DOIRISENWBIB
  • On Foundational Discretization Barriers in STFT Phase Retrieval. / Grohs, Philipp; Liehr, Lukas.
    in: Journal of Fourier Analysis and Applications, Jahrgang 28, Nr. 2, 15.04.2022, S. ARTN 39.
    DOIRISENWBIB
  • Constructive deep ReLU neural network approximation. / Herrmann, Lukas; Joost, A; Opschoor, A. et al.
    in: Journal of Scientific Computing, Nr. 90, 06.01.2022, S. Article number: 75.
    DOIRISENWBIB
  • Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies. / Verdun, Claudio M.; Fuchs, Tim; Harar, Pavol et al.
    in: Frontiers in Public Health, Jahrgang 9, 18.08.2021, S. ARTN 583377.
    DOIRISENWBIB
  • Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions. / Grohs, P.; Herrmann, L.
    in: IMA Journal of Numerical Analysis, Jahrgang tba, Nr. tba, 10.05.2021, S. tba.
    DOIRISENWBIB
  • DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing. / Elbraechter, Dennis; Grohs, Philipp; Jentzen, Arnulf et al.
    in: Constructive Approximation, 06.05.2021.
    DOIRISENWBIB
  • Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems. / Herrmann, L.; Keller, M.; Schwab, C.
    in: Mathematics of Computation, Jahrgang 90, Nr. 330, 10.03.2021, S. 1831-1860.
    DOIDownloadRISENWBIB
  • Deep Neural Network Expression of Posterior Expectations in Bayesian PDE Inversion. / Herrmann, L; Schwab, C; Zech, J.
    in: Inverse Problems, Jahrgang 36, Nr. 12, 03.12.2020, S. 125011.
    DOIDownloadRISENWBIB
  • Bilinear Pseudo-differential Operators with Gevrey-Hormander Symbols. / Abdeljawad, Ahmed; Coriasco, Sandro; Teofanov, Nenad.
    in: Mediterranean Journal of Mathematics, Jahrgang 17, Nr. 4, 27.06.2020, S. ARTN 120.
    DOIRISENWBIB
  • Characterizations of a class of Pilipovic spaces by powers of harmonic oscillator. / Abdeljawad, Ahmed; Fernandez, Carmen; Galbis, Antonio et al.
    in: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, Jahrgang 114, Nr. 3, 14.05.2020, S. ARTN 131.
    DOIRISENWBIB
  • Deterministic and stochastic Cauchy problems for a class of weakly hyperbolic operators on R-n. / Abdeljawad, Ahmed; Ascanelli, Alessia; Coriasco, Sandro.
    in: Monatshefte fur Mathematik, 21.02.2020.
    DOIRISENWBIB

Conference Contribution: Publication in Proceedings

  • Neural Networks in Local Coordinates. / Abdeljawad, Ahmed.
    2025 International Conference on Sampling Theory and Applications (SampTA). 2025. S. 1-5.
    DOIRISENWBIB
  • Multilevel Quasi-Monte Carlo Uncertainty Quantification for Advection-Diffusion-Reaction. / Herrmann, L.; Schwab, C.; L'Ecuyer, P. (Herausgeber:in) et al.
    Monte Carlo and Quasi-Monte Carlo Methods 2018. Cham: Springer, 2020. S. 31-67 (Springer Proceedings in Mathematics & Statistics).
    DOIRISENWBIB
  • Neural Networks in Local Coordinates. / Abdeljawad, Ahmed.
    2025 International Conference on Sampling Theory and Applications (SampTA). 2025. S. 1-5.
    DOIRISENWBIB
  • Multilevel Quasi-Monte Carlo Uncertainty Quantification for Advection-Diffusion-Reaction. / Herrmann, L.; Schwab, C.; L'Ecuyer, P. (Herausgeber:in) et al.
    Monte Carlo and Quasi-Monte Carlo Methods 2018. Cham: Springer, 2020. S. 31-67 (Springer Proceedings in Mathematics & Statistics).
    DOIRISENWBIB