Philipp Grohs

Institut für Geometrie, Technische Universität Graz, A8010 Graz, Austria

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Papers80 papers

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Anisotropic Multiscale Systems on Bounded Domains

P. Grohs, G. Kutyniok, J. Ma, P. Petersen, Angewandte Mathematik

Advances in Computational Mathematics, no. 2 (2020): 1-33

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Phase Retrieval: Uniqueness and Stability

Philipp Grohs, Sarah Koppensteiner, Martin Rathmair

SIAM Review, no. 2 (2020): 301-350

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Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning

Julius Berner, Markus Dablander,Philipp Grohs

NeurIPS, (2020)

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Deep Neural Network Approximation Theory

Philipp Grohs, Dmytro Perekrestenko, Dennis Elbrächter,Helmut Bölcskei

arXiv: Learning, (2019)

Cited by28EIBibtex

Optimal Approximation with Sparsely Connected Deep Neural Networks

Helmut Bölcskei,Philipp Grohs,Gitta Kutyniok, Philipp Petersen

SIMODS, (2019)

Cited by13EIBibtex

The Oracle of DLphi

Dominik Alfke, Weston Baines, Jan Blechschmidt, Mauricio J. del Razo Sarmina, Amnon Drory, Dennis Elbrächter, Nando Farchmin, Matteo Gambara, Silke Glas,Philipp Grohs, Peter Hinz, Danijel Kivaranovic

arXiv: Learning, (2019)

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Optimal Approximation with Sparsely Connected Deep Neural Networks

Helmut Bölcskei,Philipp Grohs,Gitta Kutyniok, Philipp Petersen

SIAM Journal on Mathematics of Data Science, no. 1 (2019): 8-45

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On the approximation of functions with line singularities by ridgelets

Axel Obermeier,Philipp Grohs

Journal of Approximation Theory, (2019): 30-95

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Space-time error estimates for deep neural network approximations for differential equations

Grohs Philipp, Hornung Fabian,Jentzen Arnulf, Zimmermann Philipp

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Gabor phase retrieval is severely ill-posed

Rima Alaifari,Philipp Grohs

Applied and Computational Harmonic Analysis, (2019)

Cited by4Bibtex

How degenerate is the parametrization of neural networks with the ReLU activation function

Dennis Elbrächter, Julius Berner,Philipp Grohs

NeurIPS, pp.7788-7799, (2019)

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Projection-Based Finite Elements for Nonlinear Function Spaces

Philipp Grohs, Hanne Hardering,Oliver Sander,Markus Sprecher

SIAM Journal on Numerical Analysis, no. 1 (2019): 404-428

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Towards a regularity theory for ReLU networks - chain rule and global error estimates

Julius Berner, Dennis Elbrächter,Philipp Grohs,Arnulf Jentzen

arXiv: Learning, (2019)

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How degenerate is the parametrization of neural networks with the ReLU activation function

Julius Berner, Dennis Elbrächter,Philipp Grohs

ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 32 (NIPS 2019), (2019)

Cited by7EIBibtex

Nonlinear Data: Theory and Algorithms

Philipp Grohs,Oliver Sander, Jean-Luc Starck,Johannes Wallner

Oberwolfach Reports, no. 2 (2019): 1161-1234

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Stable Gabor phase retrieval for multivariate functions

Philipp Grohs, Martin Rathmair

arXiv: Functional Analysis, (2019)

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The Mathematics of Phase Retrieval

Philipp Grohs, Sarah Koppensteiner, Martin Rathmair

arXiv: Functional Analysis, (2019)

Cited by1Bibtex

Stable Gabor Phase Retrieval and Spectral Clustering

Philipp Grohs, Martin Rathmair

Communications on Pure and Applied Mathematics, no. 5 (2019): 981-1043

Cited by3Bibtex

Solving stochastic differential equations and Kolmogorov equations by means of deep learning

Christian Beck, Sebastian Becker,Philipp Grohs, Nor Jaafari,Arnulf Jentzen

The annual research report, (2018)

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Analysis of Edge and Corner Points Using Parabolic Dictionaries

Philipp Grohs, Željko Kereta

Applied and Computational Harmonic Analysis, no. 2 (2018): 655-681

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Papers80 papers

Philipp Grohs