Smoothness Properties of Lie Group Subdivision Schemes. - Johannes Wallner 001; Esfandiar Nava Yazdani; Philipp Grohs (Multiscale Model. Simul., 2007)

Smoothness Analysis of Subdivision Schemes on Regular Grids by Proximity. - Philipp Grohs (SIAM J. Numer. Anal., 2008)

Laguerre minimal surfaces, isotropic geometry and linear elasticity. - Helmut Pottmann; Philipp Grohs; Niloy J. Mitra (Adv. Comput. Math., 2009)

Smoothness equivalence properties of univariate subdivision schemes and their projection analogues. - Philipp Grohs (Numerische Mathematik, 2009)

Edge offset meshes in Laguerre geometry. - Helmut Pottmann; Philipp Grohs; Bernhard Blaschitz (Adv. Comput. Math., 2010)

Approximation order from stability for nonlinear subdivision schemes. - Philipp Grohs (J. Approx. Theory, 2010)

Approximation order of interpolatory nonlinear subdivision schemes. - Nira Dyn; Philipp Grohs; Johannes Wallner 001 (J. Comput. Appl. Math., 2010)

A General Proximity Analysis of Nonlinear Subdivision Schemes. - Philipp Grohs (SIAM J. Math. Anal., 2010)

Definability and stability of multiscale decompositions for manifold-valued data. - Philipp Grohs; Johannes Wallner 001 (J. Frankl. Inst., 2012)

Refinable functions for dilation families. - Philipp Grohs (Adv. Comput. Math., 2013)

Geometric multiscale decompositions of dynamic low-rank matrices. - Philipp Grohs (Comput. Aided Geom. Des., 2013)

Bandlimited shearlet-type frames with nice duals. - Philipp Grohs (J. Comput. Appl. Math., 2013)

Ridgelet Methods for Linear Transport Equations. - Philipp Grohs; Axel Obermeier (Curves and Surfaces, 2014)

Parabolic Molecules. - Philipp Grohs; Gitta Kutyniok (Found. Comput. Math., 2014)

From Group Representations to Signal Analysis. - Stephan Dahlke; Filippo De Mari; Philipp Grohs; Demetrio Labate (Harmonic and Applied Analysis, 2015)

Optimally Sparse Data Representations. - Philipp Grohs (Harmonic and Applied Analysis, 2015)

Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements. - Philipp Grohs; Hanne Hardering; Oliver Sander (Found. Comput. Math., 2015)

FFRT: A Fast Finite Ridgelet Transform for Radiative Transport. - Simon Etter; Philipp Grohs; Axel Obermeier (Multiscale Model. Simul., 2015)

Discrete Deep Feature Extraction: A Theory and New Architectures. - Thomas Wiatowski; Michael Tschannen; Aleksandar Stanic; Philipp Grohs; Helmut Bölcskei (ICML, 2016)

Deep convolutional neural networks on cartoon functions. - Philipp Grohs; Thomas Wiatowski; Helmut Bölcskei (ISIT, 2016)

ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds. - Philipp Grohs; Seyedehsomayeh Hosseini (Adv. Comput. Math., 2016)

A shearlet-based fast thresholded Landweber algorithm for deconvolution. - Philipp Grohs; Zeljko Kereta; Uwe Wiesmann (Int. J. Wavelets Multiresolution Inf. Process., 2016)

Energy decay and conservation in deep convolutional neural networks. - Philipp Grohs; Thomas Wiatowski; Helmut Bölcskei (ISIT, 2017)

Topology Reduction in Deep Convolutional Feature Extraction Networks. - Thomas Wiatowski; Philipp Grohs; Helmut Bölcskei (CoRR, 2017)

Scattered manifold-valued data approximation. - Philipp Grohs; Markus Sprecher; Thomas Yu (Numerische Mathematik, 2017)

Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces. - Rima Alaifari; Philipp Grohs (SIAM J. Math. Anal., 2017)

Solving stochastic differential equations and Kolmogorov equations by means of deep learning. - Christian Beck; Sebastian Becker; Philipp Grohs; Nor Jaafari; Arnulf Jentzen (CoRR, 2018)

The universal approximation power of finite-width deep ReLU networks. - Dmytro Perekrestenko; Philipp Grohs; Dennis Elbrächter; Helmut Bölcskei (CoRR, 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)

Energy Propagation in Deep Convolutional Neural Networks. - Thomas Wiatowski; Philipp Grohs; Helmut Bölcskei (IEEE Trans. Inf. Theory, 2018)

Planting Synchronisation Trees for Discovering Interaction Patterns Among Brain Regions. - Lena Greta Marie Bauer; Philipp Grohs; Afra M. Wohlschläger; Claudia Plant (ICDM Workshops, 2019)

How degenerate is the parametrization of neural networks with the ReLU activation function? - Dennis Elbrächter; Julius Berner; Philipp Grohs (NeurIPS, 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; et al. (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)

Deep neural network approximations for Monte Carlo algorithms. - Philipp Grohs; Arnulf Jentzen; Diyora Salimova (CoRR, 2019)

Uniform error estimates for artificial neural network approximations for heat equations. - Lukas Gonon; Philipp Grohs; Arnulf Jentzen; David Kofler; David Siska (CoRR, 2019)

Stable Phase Retrieval in Infinite Dimensions. - Rima Alaifari; Ingrid Daubechies; Philipp Grohs; Rujie Yin (Found. Comput. Math., 2019)

On the approximation of functions with line singularities by ridgelets. - Axel Obermeier; Philipp Grohs (J. Approx. Theory, 2019)

Projection-Based Finite Elements for Nonlinear Function Spaces. - Philipp Grohs; Hanne Hardering; Oliver Sander; Markus Sprecher (SIAM J. Numer. Anal., 2019)

Optimal Approximation with Sparsely Connected Deep Neural Networks. - Helmut Bölcskei; Philipp Grohs; Gitta Kutyniok; Philipp Petersen (SIAM J. Math. Data Sci., 2019)

Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning. - Julius Berner; Markus Dablander; Philipp Grohs (NeurIPS, 2020)

Anisotropic multiscale systems on bounded domains. - Philipp Grohs; Gitta Kutyniok; Jackie Ma; Philipp Petersen; Mones Raslan (Adv. Comput. Math., 2020)

Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions. - Philipp Grohs; Lukas Herrmann (CoRR, 2020)

Phase Retrieval: Uniqueness and Stability. - Philipp Grohs; Sarah Koppensteiner; Martin Rathmair (SIAM Rev., 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)

Approximations with deep neural networks in Sobolev time-space. - Ahmed Abdeljawad; Philipp Grohs (CoRR, 2021)

Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations. - Philipp Grohs; Lukas Herrmann (CoRR, 2021)

The Modern Mathematics of Deep Learning. - Julius Berner; Philipp Grohs; Gitta Kutyniok; Philipp Petersen (CoRR, 2021)

Stable Gabor phase retrieval in Gaussian shift-invariant spaces via biorthogonality. - Philipp Grohs; Lukas Liehr (CoRR, 2021)

Sobolev-type embeddings for neural network approximation spaces. - Philipp Grohs; Felix Voigtländer (CoRR, 2021)

Solving the Kolmogorov PDE by Means of Deep Learning. - Christian Beck; Sebastian Becker; Philipp Grohs; Nor Jaafari; Arnulf Jentzen (J. Sci. Comput., 2021)

Deep Neural Network Approximation Theory. - Dennis Elbrächter; Dmytro Perekrestenko; Philipp Grohs; Helmut Bölcskei (IEEE Trans. Inf. Theory, 2021)

Gold-standard solutions to the Schrödinger equation using deep learning: How much physics do we need? - Leon Gerard; Michael Scherbela; Philipp Marquetand; Philipp Grohs (NeurIPS, 2022)

Training ReLU networks to high uniform accuracy is intractable. - Julius Berner; Philipp Grohs; Felix Voigtländer (CoRR, 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)

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)

Integral representations of shallow neural network with rectified power unit activation function. - Ahmed Abdeljawad; Philipp Grohs (Neural Networks, 2022)

Learning ReLU networks to high uniform accuracy is intractable. - Julius Berner; Philipp Grohs; Felix Voigtländer (ICLR, 2023)

Variational Monte Carlo on a Budget - Fine-tuning pre-trained Neural Wavefunctions. - Michael Scherbela; Leon Gerard; Philipp Grohs (NeurIPS, 2023)

Towards a Foundation Model for Neural Network Wavefunctions. - Michael Scherbela; Leon Gerard; Philipp Grohs (CoRR, 2023)

FakET: Simulating Cryo-Electron Tomograms with Neural Style Transfer. - Pavol Harár; Lukas Herrmann; Philipp Grohs; David Haselbach (CoRR, 2023)

Sampling Complexity of Deep Approximation Spaces. - Ahmed Abdeljawad; Philipp Grohs (CoRR, 2023)

Space-time error estimates for deep neural network approximations for differential equations. - Philipp Grohs; Fabian Hornung; Arnulf Jentzen; Philipp Zimmermann (Adv. Comput. Math., 2023)

Phase Transitions in Rate Distortion Theory and Deep Learning. - Philipp Grohs; Andreas Klotz; Felix Voigtländer (Found. Comput. Math., 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., 2023)

Non-Uniqueness Theory in Sampled STFT Phase Retrieval. - Philipp Grohs; Lukas Liehr (SIAM J. Math. Anal., 2023)

Transferable Neural Wavefunctions for Solids. - Leon Gerard; Michael Scherbela; Halvard Sutterud; W. Matthew C. Foulkes; Philipp Grohs (CoRR, 2024)

The sampling complexity of learning invertible residual neural networks. - Yuanyuan Li; Philipp Grohs; Philipp Petersen (CoRR, 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., 2024)

Theory-to-Practice Gap for Neural Networks and Neural Operators. - Philipp Grohs; Samuel Lanthaler; Margaret Trautner (CoRR, 2025)

Accurate Ab-initio Neural-network Solutions to Large-Scale Electronic Structure Problems. - Michael Scherbela; Nicholas Gao; Philipp Grohs; Stephan Günnemann (CoRR, 2025)

Phaseless Sampling on Square-Root Lattices. - Philipp Grohs; Lukas Liehr (Found. Comput. Math., 2025)

From completeness of discrete translates to phaseless sampling of the short-time Fourier transform. - Philipp Grohs; Lukas Liehr; Irina Shafkulovska (Adv. Comput. Math., 2025)