Philipp Grohs

According to our database1, Philipp Grohs authored at least 52 papers between 2007 and 2021.

Collaborative distances:
  • Dijkstra number2 of four.
  • Erdős number3 of four.



In proceedings 
PhD thesis 


Online presence:



Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces.
CoRR, 2021

Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations.
CoRR, 2021

Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality.
CoRR, 2021

Approximations with deep neural networks in Sobolev time-space.
CoRR, 2021

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., 2020

Phase Retrieval: Uniqueness and Stability.
SIAM Rev., 2020

Phase Transitions in Rate Distortion Theory and Deep Learning.
CoRR, 2020

Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions.
CoRR, 2020

Anisotropic multiscale systems on bounded domains.
Adv. Comput. Math., 2020

Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning.
Proceedings of the Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, 2020

Optimal Approximation with Sparsely Connected Deep Neural Networks.
SIAM J. Math. Data Sci., 2019

Projection-Based Finite Elements for Nonlinear Function Spaces.
SIAM J. Numer. Anal., 2019

On the approximation of functions with line singularities by ridgelets.
J. Approx. Theory, 2019

Stable Phase Retrieval in Infinite Dimensions.
Found. Comput. Math., 2019

Uniform error estimates for artificial neural network approximations for heat equations.
CoRR, 2019

Deep neural network approximations for Monte Carlo algorithms.
CoRR, 2019

Space-time error estimates for deep neural network approximations for differential equations.
CoRR, 2019

Towards a regularity theory for ReLU networks - chain rule and global error estimates.
CoRR, 2019

The Oracle of DLphi.
CoRR, 2019

Deep Neural Network Approximation Theory.
CoRR, 2019

How degenerate is the parametrization of neural networks with the ReLU activation function?
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.
Proceedings of the 2019 International Conference on Data Mining Workshops, 2019

Energy Propagation in Deep Convolutional Neural Networks.
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.
CoRR, 2018

The universal approximation power of finite-width deep ReLU networks.
CoRR, 2018

Solving stochastic differential equations and Kolmogorov equations by means of deep learning.
CoRR, 2018

Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces.
SIAM J. Math. Anal., 2017

Scattered manifold-valued data approximation.
Numerische Mathematik, 2017

Topology Reduction in Deep Convolutional Feature Extraction Networks.
CoRR, 2017

Energy decay and conservation in deep convolutional neural networks.
Proceedings of the 2017 IEEE International Symposium on Information Theory, 2017

A shearlet-based fast thresholded Landweber algorithm for deconvolution.
Int. J. Wavelets Multiresolution Inf. Process., 2016

ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds.
Adv. Comput. Math., 2016

Deep convolutional neural networks on cartoon functions.
Proceedings of the IEEE International Symposium on Information Theory, 2016

Discrete Deep Feature Extraction: A Theory and New Architectures.
Proceedings of the 33nd International Conference on Machine Learning, 2016

FFRT: A Fast Finite Ridgelet Transform for Radiative Transport.
Multiscale Model. Simul., 2015

Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements.
Found. Comput. Math., 2015

Optimally Sparse Data Representations.
Proceedings of the Harmonic and Applied Analysis - From Groups to Signals, 2015

From Group Representations to Signal Analysis.
Proceedings of the Harmonic and Applied Analysis - From Groups to Signals, 2015

Parabolic Molecules.
Found. Comput. Math., 2014

Ridgelet Methods for Linear Transport Equations.
Proceedings of the Curves and Surfaces, 2014

Bandlimited shearlet-type frames with nice duals.
J. Comput. Appl. Math., 2013

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

Refinable functions for dilation families.
Adv. Comput. Math., 2013

Definability and stability of multiscale decompositions for manifold-valued data.
J. Frankl. Inst., 2012

A General Proximity Analysis of Nonlinear Subdivision Schemes.
SIAM J. Math. Anal., 2010

Approximation order of interpolatory nonlinear subdivision schemes.
J. Comput. Appl. Math., 2010

Approximation order from stability for nonlinear subdivision schemes.
J. Approx. Theory, 2010

Edge offset meshes in Laguerre geometry.
Adv. Comput. Math., 2010

Smoothness equivalence properties of univariate subdivision schemes and their projection analogues.
Numerische Mathematik, 2009

Laguerre minimal surfaces, isotropic geometry and linear elasticity.
Adv. Comput. Math., 2009

Smoothness Analysis of Subdivision Schemes on Regular Grids by Proximity.
SIAM J. Numer. Anal., 2008

Smoothness Properties of Lie Group Subdivision Schemes.
Multiscale Model. Simul., 2007