Philipp Grohs

Publication Activity (10 Years)

Years Active: 2007-2024
Publications (10 Years): 66

Top Topics

Differential Equations

Error Estimates

Top Venues

Found. Comput. Math.

Adv. Comput. Math.

Publications

Philipp Grohs, Felix Voigtländer
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces. Found. Comput. Math. 24 (4) (2024)
Leon Gerard, Michael Scherbela, Halvard Sutterud, W. Matthew C. Foulkes, Philipp Grohs
Transferable Neural Wavefunctions for Solids. CoRR (2024)
Philipp Grohs, Andreas Klotz, Felix Voigtländer
Phase Transitions in Rate Distortion Theory and Deep Learning. Found. Comput. Math. 23 (1) (2023)
Michael Scherbela, Leon Gerard, Philipp Grohs
Variational Monte Carlo on a Budget - Fine-tuning pre-trained Neural Wavefunctions. NeurIPS (2023)
Philipp Grohs, Lukas Liehr
Non-Uniqueness Theory in Sampled STFT Phase Retrieval. SIAM J. Math. Anal. 55 (5) (2023)
Julius Berner, Philipp Grohs, Felix Voigtländer
Learning ReLU networks to high uniform accuracy is intractable. ICLR (2023)
Ahmed Abdeljawad, Philipp Grohs
Sampling Complexity of Deep Approximation Spaces. CoRR (2023)
Philipp Grohs, Fabian Hornung, Arnulf Jentzen, Philipp Zimmermann
Space-time error estimates for deep neural network approximations for differential equations. Adv. Comput. Math. 49 (1) (2023)
Pavol Harár, Lukas Herrmann, Philipp Grohs, David Haselbach
FakET: Simulating Cryo-Electron Tomograms with Neural Style Transfer. CoRR (2023)
Michael Scherbela, Leon Gerard, Philipp Grohs
Variational Monte Carlo on a Budget - Fine-tuning pre-trained Neural Wavefunctions. CoRR (2023)
Michael Scherbela, Leon Gerard, Philipp Grohs
Towards a Foundation Model for Neural Network Wavefunctions. CoRR (2023)
Philipp Grohs, Shokhrukh Ibragimov, Arnulf Jentzen, Sarah Koppensteiner
Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality. J. Complex. 77 (2023)
Julius Berner, Philipp Grohs, Felix Voigtländer
Training ReLU networks to high uniform accuracy is intractable. CoRR (2022)
Leon Gerard, Michael Scherbela, Philipp Marquetand, Philipp Grohs
Gold-standard solutions to the Schrödinger equation using deep learning: How much physics do we need? CoRR (2022)
Michael Scherbela, Rafael Reisenhofer, Leon Gerard, Philipp Marquetand, Philipp Grohs
Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks. Nat. Comput. Sci. 2 (5) (2022)
Ahmed Abdeljawad, Philipp Grohs
Integral representations of shallow neural network with rectified power unit activation function. Neural Networks 155 (2022)
Leon Gerard, Michael Scherbela, Philipp Marquetand, Philipp Grohs
Gold-standard solutions to the Schrödinger equation using deep learning: How much physics do we need? NeurIPS (2022)
Lena G. M. Bauer, Fabian Hirsch, Corey Jones, Matthew Hollander, Philipp Grohs, Amit Anand, Claudia Plant, Afra M. Wohlschläger
Quantification of Kuramoto Coupling Between Intrinsic Brain Networks Applied to fMRI Data in Major Depressive Disorder. Frontiers Comput. Neurosci. 16 (2022)
Ahmed Abdeljawad, Philipp Grohs
Approximations with deep neural networks in Sobolev time-space. CoRR (2021)
Philipp Grohs, Felix Voigtländer
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces. CoRR (2021)
Philipp Grohs, Lukas Liehr
Stable Gabor phase retrieval in Gaussian shift-invariant spaces via biorthogonality. CoRR (2021)
Christian Beck, Sebastian Becker, Philipp Grohs, Nor Jaafari, Arnulf Jentzen
Solving the Kolmogorov PDE by Means of Deep Learning. J. Sci. Comput. 88 (3) (2021)
Ahmed Abdeljawad, Philipp Grohs
Integral representations of shallow neural network with Rectified Power Unit activation function. CoRR (2021)
Philipp Grohs, Felix Voigtländer
Sobolev-type embeddings for neural network approximation spaces. CoRR (2021)
Philipp Grohs, Lukas Herrmann
Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations. CoRR (2021)
Philipp Grohs, Shokhrukh Ibragimov, Arnulf Jentzen, Sarah Koppensteiner
Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality. CoRR (2021)
Michael Scherbela, Rafael Reisenhofer, Leon Gerard, Philipp Marquetand, Philipp Grohs
Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks. CoRR (2021)
Dennis Elbrächter, Dmytro Perekrestenko, Philipp Grohs, Helmut Bölcskei
Deep Neural Network Approximation Theory. IEEE Trans. Inf. Theory 67 (5) (2021)
Julius Berner, Philipp Grohs, Gitta Kutyniok, Philipp Petersen
The Modern Mathematics of Deep Learning. CoRR (2021)
Julius Berner, Philipp Grohs, Arnulf Jentzen
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. SIAM J. Math. Data Sci. 2 (3) (2020)
Philipp Grohs, Lukas Herrmann
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions. CoRR (2020)
Philipp Grohs, Sarah Koppensteiner, Martin Rathmair
Phase Retrieval: Uniqueness and Stability. SIAM Rev. 62 (2) (2020)
Julius Berner, Markus Dablander, Philipp Grohs
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning. NeurIPS (2020)
Julius Berner, Markus Dablander, Philipp Grohs
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning. CoRR (2020)
Philipp Grohs, Gitta Kutyniok, Jackie Ma, Philipp Petersen, Mones Raslan
Anisotropic multiscale systems on bounded domains. Adv. Comput. Math. 46 (2) (2020)
Philipp Grohs, Andreas Klotz, Felix Voigtländer
Phase Transitions in Rate Distortion Theory and Deep Learning. CoRR (2020)
Philipp Grohs, Fabian Hornung, Arnulf Jentzen, Philipp Zimmermann
Space-time error estimates for deep neural network approximations for differential equations. CoRR (2019)
Philipp Grohs, Hanne Hardering, Oliver Sander, Markus Sprecher
Projection-Based Finite Elements for Nonlinear Function Spaces. SIAM J. Numer. Anal. 57 (1) (2019)
Rima Alaifari, Ingrid Daubechies, Philipp Grohs, Rujie Yin
Stable Phase Retrieval in Infinite Dimensions. Found. Comput. Math. 19 (4) (2019)
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
The Oracle of DLphi. CoRR (2019)
Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen
Optimal Approximation with Sparsely Connected Deep Neural Networks. SIAM J. Math. Data Sci. 1 (1) (2019)
Julius Berner, Dennis Elbrächter, Philipp Grohs
How degenerate is the parametrization of neural networks with the ReLU activation function? CoRR (2019)
Axel Obermeier, Philipp Grohs
On the approximation of functions with line singularities by ridgelets. J. Approx. Theory 237 (2019)
Philipp Grohs, Dmytro Perekrestenko, Dennis Elbrächter, Helmut Bölcskei
Deep Neural Network Approximation Theory. CoRR (2019)
Dennis Elbrächter, Julius Berner, Philipp Grohs
How degenerate is the parametrization of neural networks with the ReLU activation function? NeurIPS (2019)
Lukas Gonon, Philipp Grohs, Arnulf Jentzen, David Kofler, David Siska
Uniform error estimates for artificial neural network approximations for heat equations. CoRR (2019)
Lena Greta Marie Bauer, Philipp Grohs, Afra M. Wohlschläger, Claudia Plant
Planting Synchronisation Trees for Discovering Interaction Patterns Among Brain Regions. ICDM Workshops (2019)
Julius Berner, Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen
Towards a regularity theory for ReLU networks - chain rule and global error estimates. CoRR (2019)
Philipp Grohs, Arnulf Jentzen, Diyora Salimova
Deep neural network approximations for Monte Carlo algorithms. CoRR (2019)
Dmytro Perekrestenko, Philipp Grohs, Dennis Elbrächter, Helmut Bölcskei
The universal approximation power of finite-width deep ReLU networks. CoRR (2018)
Julius Berner, Philipp Grohs, Arnulf Jentzen
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. CoRR (2018)
Christian Beck, Sebastian Becker, Philipp Grohs, Nor Jaafari, Arnulf Jentzen
Solving stochastic differential equations and Kolmogorov equations by means of deep learning. CoRR (2018)
Thomas Wiatowski, Philipp Grohs, Helmut Bölcskei
Energy Propagation in Deep Convolutional Neural Networks. IEEE Trans. Inf. Theory 64 (7) (2018)
Philipp Grohs, Fabian Hornung, Arnulf Jentzen, Philippe von Wurstemberger
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations. CoRR (2018)
Thomas Wiatowski, Philipp Grohs, Helmut Bölcskei
Energy Propagation in Deep Convolutional Neural Networks. CoRR (2017)
Philipp Grohs, Thomas Wiatowski, Helmut Bölcskei
Energy decay and conservation in deep convolutional neural networks. ISIT (2017)
Helmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen
Optimal Approximation with Sparsely Connected Deep Neural Networks. CoRR (2017)
Rima Alaifari, Philipp Grohs
Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces. SIAM J. Math. Anal. 49 (3) (2017)
Thomas Wiatowski, Philipp Grohs, Helmut Bölcskei
Topology Reduction in Deep Convolutional Feature Extraction Networks. CoRR (2017)
Philipp Grohs, Markus Sprecher, Thomas Yu
Scattered manifold-valued data approximation. Numerische Mathematik 135 (4) (2017)
Thomas Wiatowski, Michael Tschannen, Aleksandar Stanic, Philipp Grohs, Helmut Bölcskei
Discrete Deep Feature Extraction: A Theory and New Architectures. ICML (2016)
Philipp Grohs, Seyedehsomayeh Hosseini
ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds. Adv. Comput. Math. 42 (2) (2016)
Philipp Grohs, Zeljko Kereta, Uwe Wiesmann
A shearlet-based fast thresholded Landweber algorithm for deconvolution. Int. J. Wavelets Multiresolution Inf. Process. 14 (5) (2016)
Thomas Wiatowski, Michael Tschannen, Aleksandar Stanic, Philipp Grohs, Helmut Bölcskei
Discrete Deep Feature Extraction: A Theory and New Architectures. CoRR (2016)
Philipp Grohs, Thomas Wiatowski, Helmut Bölcskei
Deep Convolutional Neural Networks on Cartoon Functions. CoRR (2016)
Philipp Grohs, Thomas Wiatowski, Helmut Bölcskei
Deep convolutional neural networks on cartoon functions. ISIT (2016)
Philipp Grohs, Hanne Hardering, Oliver Sander
Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements. Found. Comput. Math. 15 (6) (2015)
Simon Etter, Philipp Grohs, Axel Obermeier
FFRT: A Fast Finite Ridgelet Transform for Radiative Transport. Multiscale Model. Simul. 13 (1) (2015)
Philipp Grohs, Axel Obermeier
Ridgelet Methods for Linear Transport Equations. Curves and Surfaces (2014)
Philipp Grohs, Gitta Kutyniok
Parabolic Molecules. Found. Comput. Math. 14 (2) (2014)
Philipp Grohs
Refinable functions for dilation families. Adv. Comput. Math. 38 (3) (2013)
Philipp Grohs
Bandlimited shearlet-type frames with nice duals. J. Comput. Appl. Math. 243 (2013)
Philipp Grohs
Geometric multiscale decompositions of dynamic low-rank matrices. Comput. Aided Geom. Des. 30 (8) (2013)
Philipp Grohs, Johannes Wallner
Definability and stability of multiscale decompositions for manifold-valued data. J. Frankl. Inst. 349 (5) (2012)
Philipp Grohs
Approximation order from stability for nonlinear subdivision schemes. J. Approx. Theory 162 (5) (2010)
Philipp Grohs
A General Proximity Analysis of Nonlinear Subdivision Schemes. SIAM J. Math. Anal. 42 (2) (2010)
Helmut Pottmann, Philipp Grohs, Bernhard Blaschitz
Edge offset meshes in Laguerre geometry. Adv. Comput. Math. 33 (1) (2010)
Nira Dyn, Philipp Grohs, Johannes Wallner
Approximation order of interpolatory nonlinear subdivision schemes. J. Comput. Appl. Math. 233 (7) (2010)
Helmut Pottmann, Philipp Grohs, Niloy J. Mitra
Laguerre minimal surfaces, isotropic geometry and linear elasticity. Adv. Comput. Math. 31 (4) (2009)
Philipp Grohs
Smoothness equivalence properties of univariate subdivision schemes and their projection analogues. Numerische Mathematik 113 (2) (2009)
Philipp Grohs
Smoothness Analysis of Subdivision Schemes on Regular Grids by Proximity. SIAM J. Numer. Anal. 46 (4) (2008)
Johannes Wallner, Esfandiar Nava Yazdani, Philipp Grohs
Smoothness Properties of Lie Group Subdivision Schemes. Multiscale Model. Simul. 6 (2) (2007)