Philipp Grohs

According to our database, Philipp Grohs authored at least 69 papers between 2007 and 2024.

Collaborative distances:

• Dijkstra number of four.
• Erdős number of four.

2024

Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces.

Philipp Grohs, Felix Voigtländer

Found. Comput. Math., August, 2024

The sampling complexity of learning invertible residual neural networks.

Yuanyuan Li, Philipp Grohs, Philipp Petersen

CoRR, 2024

Transferable Neural Wavefunctions for Solids.

Leon Gerard, Michael Scherbela, Halvard Sutterud, W. Matthew C. Foulkes, Philipp Grohs

CoRR, 2024

2023

Non-Uniqueness Theory in Sampled STFT Phase Retrieval.

Philipp Grohs, Lukas Liehr

SIAM J. Math. Anal., October, 2023

Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality.

Philipp Grohs, Shokhrukh Ibragimov, Arnulf Jentzen, Sarah Koppensteiner

J. Complex., August, 2023

Phase Transitions in Rate Distortion Theory and Deep Learning.

Philipp Grohs, Andreas Klotz, Felix Voigtländer

Found. Comput. Math., February, 2023

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

Philipp Grohs, Fabian Hornung, Arnulf Jentzen, Philipp Zimmermann

Adv. Comput. Math., February, 2023

Sampling Complexity of Deep Approximation Spaces.

Ahmed Abdeljawad, Philipp Grohs

CoRR, 2023

FakET: Simulating Cryo-Electron Tomograms with Neural Style Transfer.

Pavol Harár, Lukas Herrmann, Philipp Grohs, David Haselbach

CoRR, 2023

Towards a Foundation Model for Neural Network Wavefunctions.

Michael Scherbela, Leon Gerard, Philipp Grohs

CoRR, 2023

Variational Monte Carlo on a Budget - Fine-tuning pre-trained Neural Wavefunctions.

Michael Scherbela, Leon Gerard, Philipp Grohs

Proceedings of the Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, 2023

Learning ReLU networks to high uniform accuracy is intractable.

Julius Berner, Philipp Grohs, Felix Voigtländer

Proceedings of the Eleventh International Conference on Learning Representations, 2023

2022

Integral representations of shallow neural network with rectified power unit activation function.

Ahmed Abdeljawad, Philipp Grohs

Neural Networks, 2022

Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks.

Michael Scherbela, Rafael Reisenhofer, Leon Gerard, Philipp Marquetand, Philipp Grohs

Nat. Comput. Sci., 2022

Quantification of Kuramoto Coupling Between Intrinsic Brain Networks Applied to fMRI Data in Major Depressive Disorder.

Lena G. M. Bauer, Fabian Hirsch, Corey Jones, Matthew Hollander, Philipp Grohs, Amit Anand, Claudia Plant, Afra M. Wohlschläger

Frontiers Comput. Neurosci., 2022

Training ReLU networks to high uniform accuracy is intractable.

Julius Berner, Philipp Grohs, Felix Voigtländer

CoRR, 2022

Gold-standard solutions to the Schrödinger equation using deep learning: How much physics do we need?

Leon Gerard, Michael Scherbela, Philipp Marquetand, Philipp Grohs

Proceedings of the Advances in Neural Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, 2022

2021

Deep Neural Network Approximation Theory.

Dennis Elbrächter, Dmytro Perekrestenko, Philipp Grohs, Helmut Bölcskei

IEEE Trans. Inf. Theory, 2021

Solving the Kolmogorov PDE by Means of Deep Learning.

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

J. Sci. Comput., 2021

Sobolev-type embeddings for neural network approximation spaces.

Philipp Grohs, Felix Voigtländer

CoRR, 2021

Stable Gabor phase retrieval in Gaussian shift-invariant spaces via biorthogonality.

Philipp Grohs, Lukas Liehr

CoRR, 2021

The Modern Mathematics of Deep Learning.

Julius Berner, Philipp Grohs, Gitta Kutyniok, Philipp Petersen

CoRR, 2021

Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations.

Philipp Grohs, Lukas Herrmann

CoRR, 2021

Approximations with deep neural networks in Sobolev time-space.

Ahmed Abdeljawad, Philipp Grohs

CoRR, 2021

2020

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.

Julius Berner, Philipp Grohs, Arnulf Jentzen

SIAM J. Math. Data Sci., 2020

Phase Retrieval: Uniqueness and Stability.

Philipp Grohs, Sarah Koppensteiner, Martin Rathmair

SIAM Rev., 2020

Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions.

Philipp Grohs, Lukas Herrmann

CoRR, 2020

Anisotropic multiscale systems on bounded domains.

Philipp Grohs, Gitta Kutyniok, Jackie Ma, Philipp Petersen, Mones Raslan

Adv. Comput. Math., 2020

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

Julius Berner, Markus Dablander, Philipp Grohs

Proceedings of the Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, 2020

2019

Optimal Approximation with Sparsely Connected Deep Neural Networks.

Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen

SIAM J. Math. Data Sci., 2019

Projection-Based Finite Elements for Nonlinear Function Spaces.

Philipp Grohs, Hanne Hardering, Oliver Sander, Markus Sprecher

SIAM J. Numer. Anal., 2019

On the approximation of functions with line singularities by ridgelets.

Axel Obermeier, Philipp Grohs

J. Approx. Theory, 2019

Stable Phase Retrieval in Infinite Dimensions.

Rima Alaifari, Ingrid Daubechies, Philipp Grohs, Rujie Yin

Found. Comput. Math., 2019

Uniform error estimates for artificial neural network approximations for heat equations.

Lukas Gonon, Philipp Grohs, Arnulf Jentzen, David Kofler, David Siska

CoRR, 2019

Deep neural network approximations for Monte Carlo algorithms.

Philipp Grohs, Arnulf Jentzen, Diyora Salimova

CoRR, 2019

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

Julius Berner, Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen

CoRR, 2019

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, Christian Kümmerle, Gitta Kutyniok, Sebastian Lunz, Jan MacDonald, Ryan Malthaner, Gregory Naisat, Ariel Neufeld, Philipp Christian Petersen, Rafael Reisenhofer, Jun-Da Sheng, Laura Thesing, Philipp Trunschke, Johannes von Lindheim, David Weber, Melanie Weber

CoRR, 2019

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

Dennis Elbrächter, Julius Berner, Philipp Grohs

Proceedings of the Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, 2019

Planting Synchronisation Trees for Discovering Interaction Patterns Among Brain Regions.

Lena Greta Marie Bauer, Philipp Grohs, Afra M. Wohlschläger, Claudia Plant

Proceedings of the 2019 International Conference on Data Mining Workshops, 2019

2018

Energy Propagation in Deep Convolutional Neural Networks.

Thomas Wiatowski, Philipp Grohs, Helmut Bölcskei

IEEE Trans. Inf. Theory, 2018

A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations.

Philipp Grohs, Fabian Hornung, Arnulf Jentzen, Philippe von Wurstemberger

CoRR, 2018

The universal approximation power of finite-width deep ReLU networks.

Dmytro Perekrestenko, Philipp Grohs, Dennis Elbrächter, Helmut Bölcskei

CoRR, 2018

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

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

CoRR, 2018

2017

Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces.

Rima Alaifari, Philipp Grohs

SIAM J. Math. Anal., 2017

Scattered manifold-valued data approximation.

Philipp Grohs, Markus Sprecher, Thomas Yu

Numerische Mathematik, 2017

Topology Reduction in Deep Convolutional Feature Extraction Networks.

Thomas Wiatowski, Philipp Grohs, Helmut Bölcskei

CoRR, 2017

Energy decay and conservation in deep convolutional neural networks.

Philipp Grohs, Thomas Wiatowski, Helmut Bölcskei

Proceedings of the 2017 IEEE International Symposium on Information Theory, 2017

2016

A shearlet-based fast thresholded Landweber algorithm for deconvolution.

Philipp Grohs, Zeljko Kereta, Uwe Wiesmann

Int. J. Wavelets Multiresolution Inf. Process., 2016

ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds.

Philipp Grohs, Seyedehsomayeh Hosseini

Adv. Comput. Math., 2016

Deep convolutional neural networks on cartoon functions.

Philipp Grohs, Thomas Wiatowski, Helmut Bölcskei

Proceedings of the IEEE International Symposium on Information Theory, 2016

Discrete Deep Feature Extraction: A Theory and New Architectures.

Thomas Wiatowski, Michael Tschannen, Aleksandar Stanic, Philipp Grohs, Helmut Bölcskei

Proceedings of the 33nd International Conference on Machine Learning, 2016

2015

FFRT: A Fast Finite Ridgelet Transform for Radiative Transport.

Simon Etter, Philipp Grohs, Axel Obermeier

Multiscale Model. Simul., 2015

Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements.

Philipp Grohs, Hanne Hardering, Oliver Sander

Found. Comput. Math., 2015

Optimally Sparse Data Representations.

Philipp Grohs

Proceedings of the Harmonic and Applied Analysis - From Groups to Signals, 2015

From Group Representations to Signal Analysis.

Stephan Dahlke, Filippo De Mari, Philipp Grohs, Demetrio Labate

Proceedings of the Harmonic and Applied Analysis - From Groups to Signals, 2015

2014

Parabolic Molecules.

Philipp Grohs, Gitta Kutyniok

Found. Comput. Math., 2014

Ridgelet Methods for Linear Transport Equations.

Philipp Grohs, Axel Obermeier

Proceedings of the Curves and Surfaces, 2014

2013

Bandlimited shearlet-type frames with nice duals.

Philipp Grohs

J. Comput. Appl. Math., 2013

Geometric multiscale decompositions of dynamic low-rank matrices.

Philipp Grohs

Comput. Aided Geom. Des., 2013

Refinable functions for dilation families.

Philipp Grohs

Adv. Comput. Math., 2013

2012

Definability and stability of multiscale decompositions for manifold-valued data.

Philipp Grohs, Johannes Wallner

J. Frankl. Inst., 2012

2010

A General Proximity Analysis of Nonlinear Subdivision Schemes.

Philipp Grohs

SIAM J. Math. Anal., 2010

Approximation order of interpolatory nonlinear subdivision schemes.

Nira Dyn, Philipp Grohs, Johannes Wallner

J. Comput. Appl. Math., 2010

Approximation order from stability for nonlinear subdivision schemes.

Philipp Grohs

J. Approx. Theory, 2010

Edge offset meshes in Laguerre geometry.

Helmut Pottmann, Philipp Grohs, Bernhard Blaschitz

Adv. Comput. Math., 2010

2009

Smoothness equivalence properties of univariate subdivision schemes and their projection analogues.

Philipp Grohs

Numerische Mathematik, 2009

Laguerre minimal surfaces, isotropic geometry and linear elasticity.

Helmut Pottmann, Philipp Grohs, Niloy J. Mitra

Adv. Comput. Math., 2009

2008

Smoothness Analysis of Subdivision Schemes on Regular Grids by Proximity.

Philipp Grohs

SIAM J. Numer. Anal., 2008

2007

Smoothness Properties of Lie Group Subdivision Schemes.

Johannes Wallner, Esfandiar Nava Yazdani, Philipp Grohs

Multiscale Model. Simul., 2007