Peer Reviewed Journal Publication

  • Gerard, Leon; Grohs, Philipp; Scherbela, Michael (2024) Deep learning variational Monte Carlo for solving the electronic Schrödinger equation. Handbook of Numerical Analysis, Bd. 25, S. 231-292.
    DOIRISENWBIB
  • Abdeljawad, Ahmed; Grohs, Philipp (2024) Sampling Complexity of Deep Approximation Spaces. Analysis and Applications, Bd. 23 (01), S. 1-30.
    DOIWebsiteDownloadRISENWBIB
  • Grohs, Philipp; Liehr, Lukas (2024) Phaseless Sampling on Square-Root Lattices. FOUND COMPUT MATH.
    DOIRISENWBIB
  • Scherbela, Michael; Gerard, Leon; Grohs, Philipp (2024) Towards a transferable fermionic neural wavefunction for molecules. NATURE COMMUNICATIONS, Bd. 15 (1), S. ARTN 120.
    DOIRISENWBIB
  • Dick, J.; Ebert, A.; Herrmann, L.; Kritzer, P.; Longo, M. (online: 2023) The fast reduced QMC matrix-vector product. Journal of Computational and Applied Mathematics, Bd. 440, S. 115642.
    RISENWBIB
  • Grohs, Philipp; Liehr, Lukas (2023) Stable Gabor Phase Retrieval in Gaussian Shift-Invariant Spaces via Biorthogonality. CONSTR APPROX.
    DOIRISENWBIB
  • Grohs, Philipp; Ibragimov, Shokhrukh; Jentzen, Arnulf; Koppensteiner, Sarah (2023) Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality. J COMPLEXITY, Bd. 77, S. ARTN 101746.
    DOIRISENWBIB
  • Grohs, Philipp; Voigtlaender, Felix (2023) Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces. FOUND COMPUT MATH.
    DOIRISENWBIB
  • Grohs, Philipp; Liehr, Lukas (2023) NON-UNIQUENESS THEORY IN SAMPLED STFT PHASE RETRIEVAL. SIAM J MATH ANAL, Bd. 55 (5), S. 4695-4726.
    DOIRISENWBIB
  • Schneckenreither, Guenter; Herrmann, Lukas; Reisenhofer, Rafael; Popper, Niki; Grohs, Philipp (2023) Assessing the heterogeneity in the transmission of infectious diseases from time series of epidemiological data. PLOS ONE, Bd. 18 (5).
    DOIRISENWBIB
  • Grohs, Philipp; Hornung, Fabian; Jentzen, Arnulf; von Wurstemberger, Philippe (2023) A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations. MEM AM MATH SOC, Bd. 284 (1410), S. 1-106.
    DOIRISENWBIB
  • Grohs, Philipp; Voigtlaender, Felix (2023) Sobolev-Type Embeddings for Neural Network Approximation Spaces. CONSTR APPROX.
    DOIRISENWBIB
  • Grohs, Philipp; Liehr, Lukas (2023) Injectivity of Gabor phase retrieval from lattice measurements. APPL COMPUT HARMON A, Bd. 62, S. 173-193.
    DOIRISENWBIB
  • Abdeljawad, Ahmed; Grohs, Philipp (2022) Integral representations of shallow neural network with rectified power unit activation function. Neural Netw., Bd. 155, S. 536-550.
    DOIRISENWBIB
  • Grohs, Philipp; Rathmair, Martin (2022) Stable Gabor phase retrieval for multivariate functions. J. Eur. Math. Soc., Bd. 24 (5), S. 1593-1615.
    DOIRISENWBIB
  • Scherbela, Michael; Reisenhofer, Rafael; Gerard, Leon; Marquetand, Philipp; Grohs, Philipp (2022) Solving the electronic Schrodinger equation for multiple nuclear geometries with weight-sharing deep neural networks. NATURE COMPUTATIONAL SCIENCE, Bd. 2 (5), S. 331-341.
    DOIRISENWBIB
  • Abdeljawad, Ahmed; Grohs, Philipp (2022) Approximations with deep neural networks in Sobolev time-space. Anal. Appl., Bd. 20 (03), S. 499-541.
    DOIRISENWBIB
  • Grohs, Philipp; Liehr, Lukas (2022) On Foundational Discretization Barriers in STFT Phase Retrieval. J. Fourier Anal. Appl., Bd. 28 (2), S. ARTN 39.
    DOIRISENWBIB
  • Lukas Herrmann, Joost A.A. Opschoor, Christoph Schwab (online: 2022) Constructive deep ReLU neural network approximation. Journal of Scientific Computing (90), S. Article number: 75.
    DOIDownloadRISENWBIB
  • Verdun, Claudio M.; Fuchs, Tim; Harar, Pavol; Elbrachter, Dennis; Fischer, David S. et al. [..] (2021) Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies. FRONTIERS IN PUBLIC HEALTH, Bd. 9, S. ARTN 583377.
    DOIRISENWBIB
  • P. Grohs, L. Herrmann (online: 2021) Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions. IMA Journal of Numerical Analysis, Bd. tba (tba), S. tba.
    DOIDownloadRISENWBIB
  • Elbraechter, Dennis; Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph (2021) DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing. Constr. Approx.
    DOIRISENWBIB
  • L. Herrmann, M. Keller, C. Schwab (online: 2021) Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems. Mathematics of Computation, Bd. 90 (330), S. 1831-1860.
    DOIDownloadRISENWBIB
  • L Herrmann, C Schwab, J Zech (2020) Deep Neural Network Expression of Posterior Expectations in Bayesian PDE Inversion. Inverse Problems, Bd. 36 (12), S. 125011.
    DOIDownloadRISENWBIB
  • Gerard, Leon; Grohs, Philipp; Scherbela, Michael (2024) Deep learning variational Monte Carlo for solving the electronic Schrödinger equation. Handbook of Numerical Analysis, Bd. 25, S. 231-292.
    DOIRISENWBIB
  • Abdeljawad, Ahmed; Grohs, Philipp (2024) Sampling Complexity of Deep Approximation Spaces. Analysis and Applications, Bd. 23 (01), S. 1-30.
    DOIWebsiteDownloadRISENWBIB
  • Grohs, Philipp; Liehr, Lukas (2024) Phaseless Sampling on Square-Root Lattices. FOUND COMPUT MATH.
    DOIRISENWBIB
  • Scherbela, Michael; Gerard, Leon; Grohs, Philipp (2024) Towards a transferable fermionic neural wavefunction for molecules. NATURE COMMUNICATIONS, Bd. 15 (1), S. ARTN 120.
    DOIRISENWBIB
  • Dick, J.; Ebert, A.; Herrmann, L.; Kritzer, P.; Longo, M. (online: 2023) The fast reduced QMC matrix-vector product. Journal of Computational and Applied Mathematics, Bd. 440, S. 115642.
    RISENWBIB
  • Grohs, Philipp; Liehr, Lukas (2023) Stable Gabor Phase Retrieval in Gaussian Shift-Invariant Spaces via Biorthogonality. CONSTR APPROX.
    DOIRISENWBIB
  • Grohs, Philipp; Ibragimov, Shokhrukh; Jentzen, Arnulf; Koppensteiner, Sarah (2023) Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality. J COMPLEXITY, Bd. 77, S. ARTN 101746.
    DOIRISENWBIB
  • Grohs, Philipp; Voigtlaender, Felix (2023) Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces. FOUND COMPUT MATH.
    DOIRISENWBIB
  • Grohs, Philipp; Liehr, Lukas (2023) NON-UNIQUENESS THEORY IN SAMPLED STFT PHASE RETRIEVAL. SIAM J MATH ANAL, Bd. 55 (5), S. 4695-4726.
    DOIRISENWBIB
  • Schneckenreither, Guenter; Herrmann, Lukas; Reisenhofer, Rafael; Popper, Niki; Grohs, Philipp (2023) Assessing the heterogeneity in the transmission of infectious diseases from time series of epidemiological data. PLOS ONE, Bd. 18 (5).
    DOIRISENWBIB
  • Grohs, Philipp; Hornung, Fabian; Jentzen, Arnulf; von Wurstemberger, Philippe (2023) A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations. MEM AM MATH SOC, Bd. 284 (1410), S. 1-106.
    DOIRISENWBIB
  • Grohs, Philipp; Voigtlaender, Felix (2023) Sobolev-Type Embeddings for Neural Network Approximation Spaces. CONSTR APPROX.
    DOIRISENWBIB
  • Grohs, Philipp; Liehr, Lukas (2023) Injectivity of Gabor phase retrieval from lattice measurements. APPL COMPUT HARMON A, Bd. 62, S. 173-193.
    DOIRISENWBIB
  • Abdeljawad, Ahmed; Grohs, Philipp (2022) Integral representations of shallow neural network with rectified power unit activation function. Neural Netw., Bd. 155, S. 536-550.
    DOIRISENWBIB
  • Grohs, Philipp; Rathmair, Martin (2022) Stable Gabor phase retrieval for multivariate functions. J. Eur. Math. Soc., Bd. 24 (5), S. 1593-1615.
    DOIRISENWBIB
  • Scherbela, Michael; Reisenhofer, Rafael; Gerard, Leon; Marquetand, Philipp; Grohs, Philipp (2022) Solving the electronic Schrodinger equation for multiple nuclear geometries with weight-sharing deep neural networks. NATURE COMPUTATIONAL SCIENCE, Bd. 2 (5), S. 331-341.
    DOIRISENWBIB
  • Abdeljawad, Ahmed; Grohs, Philipp (2022) Approximations with deep neural networks in Sobolev time-space. Anal. Appl., Bd. 20 (03), S. 499-541.
    DOIRISENWBIB
  • Grohs, Philipp; Liehr, Lukas (2022) On Foundational Discretization Barriers in STFT Phase Retrieval. J. Fourier Anal. Appl., Bd. 28 (2), S. ARTN 39.
    DOIRISENWBIB
  • Lukas Herrmann, Joost A.A. Opschoor, Christoph Schwab (online: 2022) Constructive deep ReLU neural network approximation. Journal of Scientific Computing (90), S. Article number: 75.
    DOIDownloadRISENWBIB
  • Verdun, Claudio M.; Fuchs, Tim; Harar, Pavol; Elbrachter, Dennis; Fischer, David S. et al. [..] (2021) Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies. FRONTIERS IN PUBLIC HEALTH, Bd. 9, S. ARTN 583377.
    DOIRISENWBIB
  • P. Grohs, L. Herrmann (online: 2021) Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions. IMA Journal of Numerical Analysis, Bd. tba (tba), S. tba.
    DOIDownloadRISENWBIB
  • Elbraechter, Dennis; Grohs, Philipp; Jentzen, Arnulf; Schwab, Christoph (2021) DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing. Constr. Approx.
    DOIRISENWBIB
  • L. Herrmann, M. Keller, C. Schwab (online: 2021) Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems. Mathematics of Computation, Bd. 90 (330), S. 1831-1860.
    DOIDownloadRISENWBIB
  • L Herrmann, C Schwab, J Zech (2020) Deep Neural Network Expression of Posterior Expectations in Bayesian PDE Inversion. Inverse Problems, Bd. 36 (12), S. 125011.
    DOIDownloadRISENWBIB

Conference Contribution: Publication in Proceedings

  • L. Herrmann, C. Schwab (2020) Multilevel Quasi-Monte Carlo Uncertainty Quantification for Advection-Diffusion-Reaction. In: L'Ecuyer, P.; Tuffin, B. (Hrsg.), Monte Carlo and Quasi-Monte Carlo Methods 2018; Cham: Springer, S. 31-67.
    DOIDownloadRISENWBIB
  • L. Herrmann, C. Schwab (2020) Multilevel Quasi-Monte Carlo Uncertainty Quantification for Advection-Diffusion-Reaction. In: L'Ecuyer, P.; Tuffin, B. (Hrsg.), Monte Carlo and Quasi-Monte Carlo Methods 2018; Cham: Springer, S. 31-67.
    DOIDownloadRISENWBIB