Publications

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, 2022.

Publications: Contribution to journal › Article › Peer Reviewed

Stable Gabor phase retrieval for multivariate functions. / Grohs, Philipp; Rathmair, Martin.
In: Journal of the European Mathematical Society, Vol. 24, No. 5, 2022, p. 1593-1615.

Publications: Contribution to journal › Article › Peer Reviewed

RICAM, the Johann Radon Institute for Computational and Applied Mathematics. / Grohs, Philipp; Kritzer, Peter; Kunisch, Karl et al.
In: EMS magazine, No. 122, 12.2021, p. 46-51.

Publications: Contribution to journal › Article

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; Harár, Pavol et al.
In: Frontiers in Public Health, Vol. 9, 583377, 18.08.2021.

Publications: Contribution to journal › Article › Peer Reviewed

Deep Neural Network Approximation Theory. / Elbrächter, Dennis; Perekrestenko, Dmytro ; Grohs, Philipp et al.
In: IEEE TRANSACTIONS ON INFORMATION THEORY, Vol. 67, No. 5, 9363169, 05.2021, p. 2581-2623.

Publications: Contribution to journal › Article › Peer Reviewed

Gabor Phase Retrieval is Severely Ill-Posed. / Alaifari, Rima; Grohs, Philipp.
In: Applied and Computational Harmonic Analysis, Vol. 50, 01.2021, p. 401-419.

Publications: Contribution to journal › Article › Peer Reviewed

Error bounds for the numerical evaluation of Legendre polynomials by a three-term recurrence. / Hrycak, Tomasz; Schmutzhard-Höfler, Sebastian.
In: Electronic Transactions on Numerical Analysis, Vol. 54, 2021, p. 323-332.

Publications: Contribution to journal › Article › Peer Reviewed

Phase Distortion by Linear Signal Transforms. / Filbir, Frank; Liehr, Lukas (Corresponding author).
In: Frontiers in Applied Mathematics and Statistics, Vol. 6, 556585, 12.11.2020.

Publications: Contribution to journal › Article › Peer Reviewed

Towards robust voice pathology detection: Investigation of supervised deep learning, gradient boosting, and anomaly detection approaches across four databases. / Harar, Pavol; Galaz, Zoltan; Alonso-Hernandez, Jesus B et al.
In: Neural Computing and Applications, Vol. 32, No. 20, 10.2020, p. 15747-15757.

Publications: Contribution to journal › Article › Peer Reviewed

Anisotropic Multiscale Systems on Bounded Domains. / Grohs, Philipp; Kutyniok, Gitta; Ma, Jackie et al.
In: Advances in Computational Mathematics, Vol. 46, 39, 13.04.2020.

Publications: Contribution to journal › Article › Peer Reviewed

On Orthogonal Projections for Dimension Reduction and Applications in Augmented Target Loss Functions for Learning Problems. / Breger, A.; Orlando, J. I.; Harar, P. et al.
In: Journal of Mathematical Imaging and Vision, Vol. 62, No. 3, 04.2020, p. 376–394.

Publications: Contribution to journal › Article › Peer Reviewed

Analysis of edge and corner points using parabolic dictionaries. / Grohs, Philipp.
In: Applied and Computational Harmonic Analysis, Vol. 48, No. 2, 03.2020, p. 655-681.

Publications: Contribution to journal › Article › Peer Reviewed

On the mathematical validity of the Higuchi method. / Liehr, L.; Massopust, P. (Corresponding author).
In: Physica D: Nonlinear Phenomena, Vol. 402, 132265, 15.01.2020.

Publications: Contribution to journal › Article › Peer Reviewed

Evaluation of Legendre polynomials by a three-term recurrence in floating-point arithmetic. / Hrycak, Tomasz (Corresponding author); Schmutzhard-Höfler, Sebastian.
In: IMA Journal of Numerical Analysis, Vol. 40, No. 1, 01.01.2020, p. 587–605.

Publications: Contribution to journal › Article › Peer Reviewed

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. / Berner, Julius; Grohs, Philipp; Jentzen, Arnulf.
In: SIAM Journal on Mathematics of Data Science, Vol. 2, No. 3, 2020, p. 631-657.

Publications: Contribution to journal › Article › Peer Reviewed

Handbook of Variational Methods for Nonlinear Geometric Data. / Grohs, Philipp (Editor); Holler, Martin (Editor); Weinmann, Andreas (Editor).
Cham: Springer, 2020. 701 p.

Publications: Book › Collection › Peer Reviewed

Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning. / Berner, Julius; Dablander, Markus; Grohs, Philipp.
Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual. ed. / H. Larochelle; M. Ranzato; R. Hadsell; M.F. Balcan; H. Lin. Cambridge, Mass.: MIT Press, 2020. (Advances in neural information processing systems : ... proceedings of the ... conference, Vol. 33).

Publications: Contribution to book › Contribution to proceedings › Peer Reviewed

Phase Retrieval: Uniqueness and Stability. / Grohs, Philipp; Koppensteiner, Sarah; Rathmair, Martin.
In: SIAM Review, Vol. 62, No. 2, 2020, p. 301-350.

Publications: Contribution to journal › Article › Peer Reviewed

Solving stochastic differential equations and Kolmogorov equations by means of deep learning. / Beck, Christian; Becker, Sebastian; Grohs, Philipp et al.
In: Journal of Scientific Computing, 2020.

Publications: Contribution to journal › Article › Peer Reviewed

Planting Synchronisation Trees for Discovering Interaction Patterns among Brain Regions. / Bauer, Lena ; Grohs, Philipp; Wohlschläger, Afra et al.
Proceedings - 19th IEEE International Conference on Data Mining Workshops, ICDMW 2019: 8–11 November 2019 Beijing, China. ed. / Panagiotis Papapetrou; Xueqi Cheng; Qing He. Piscataway, NJ: IEEE, 2019. p. 1035-1036 8955527 (International Conference on Data Mining workshops).

Publications: Contribution to book › Contribution to proceedings › Peer Reviewed