2026 Philipp Grohs: Mathematics Researcher – H-Index, Publications & Awards

Overview

Philipp Grohs is affiliated with the University of Vienna in Austria. Their research primarily spans the fields of Computer Science and Physics and Astronomy, with a significant focus on several subfields and topics connecting deep learning, neural networks, and applied mathematics.

Grohs's main subfields of study include:

Artificial Intelligence
Statistical and Nonlinear Physics
Geophysics
Radiation
Computer Vision and Pattern Recognition

Their work covers a variety of research topics, notably:

Model Reduction and Neural Networks
Neural Networks and Applications
Seismic Imaging and Inversion Techniques
Advanced X-ray Imaging Techniques
Machine Learning in Materials Science
Stochastic processes and financial applications
Mathematical Analysis and Transform Methods

Grohs has contributed to numerous publications throughout their career. Some recent representative papers include:

A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations (2023, Memoirs of the American Mathematical Society)
DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing (2021, Constructive Approximation)
Deep Neural Network Approximation Theory (2021, IEEE Transactions on Information Theory)
Group Testing for SARS-CoV-2 Allows for Up to 10-Fold Efficiency Increase Across Realistic Scenarios and Testing Strategies (2021, Frontiers in Public Health)
Space-time error estimates for deep neural network approximations for differential equations (2023, Advances in Computational Mathematics)

In addition to articles, Grohs has published books, notably through Cambridge University Press, including Mathematical Aspects of Deep Learning (2022).

Their publication record shows frequent appearances in venues such as:

arXiv (Cornell University)
Constructive Approximation
Foundations of Computational Mathematics
Advances in Computational Mathematics
IMA Journal of Numerical Analysis

Common collaborators in Grohs's research include:

Lukas Liehr
Julius Berner
Arnulf Jentzen
Michael Scherbela
Leon Gerard

Best Publications

Optimal Approximation with Sparsely Connected Deep Neural Networks

Helmut Bölcskei;Philipp Grohs;Gitta Kutyniok;Philipp Petersen

255
Citations
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

235
Citations
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

234
Citations
Deep Neural Network Approximation Theory

Dennis Elbrachter;Dmytro Perekrestenko;Philipp Grohs;Helmut Bolcskei

190
Citations
Solving stochastic differential equations and Kolmogorov equations by means of deep learning.

Christian Beck;Sebastian Becker;Philipp Grohs;Nor Jaafari

153
Citations
DNN Expression Rate Analysis of High-Dimensional PDEs: Application to Option Pricing

Dennis Elbrächter;Philipp Grohs;Philipp Grohs;Arnulf Jentzen;Arnulf Jentzen;Christoph Schwab

128
Citations
Laguerre minimal surfaces, isotropic geometry and linear elasticity

Helmut Pottmann;Philipp Grohs;Niloy J. Mitra

88
Citations
Parabolic Molecules

Philipp Grohs;Gitta Kutyniok

87
Citations
Solving the Kolmogorov PDE by Means of Deep Learning

Christian Beck;Sebastian Becker;Philipp Grohs;Nor Jaafari

85
Citations
The Modern Mathematics of Deep Learning

Julius Berner;Philipp Grohs;Gitta Kutyniok;Philipp Petersen

85
Citations
Phase Retrieval: Uniqueness and Stability

Philipp Grohs;Sarah Koppensteiner;Martin Rathmair

75
Citations
Continuous shearlet frames and resolution of the wavefront set

Philipp Grohs

72
Citations
ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds

P. Grohs;S. Hosseini

69
Citations
Stable Phase Retrieval in Infinite Dimensions

Rima Alaifari;Ingrid Daubechies;Philipp Grohs;Rujie Yin

67
Citations
Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces

Rima Alaifari;Philipp Grohs

63
Citations
Stable Gabor Phase Retrieval and Spectral Clustering

Philipp Grohs;Martin Rathmair

59
Citations
Smoothness Properties of Lie Group Subdivision Schemes

J. Wallner;E. Nava Yazdani;P. Grohs

56
Citations
Nonsmooth trust region algorithms for locally Lipschitz functions on Riemannian manifolds

P. Grohs;S. Hosseini

47
Citations
A General Proximity Analysis of Nonlinear Subdivision Schemes

Philipp Grohs

44
Citations
Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements

Philipp Grohs;Hanne Hardering;Oliver Sander

29
Citations

Frequent Co-Authors

Arnulf Jentzen Chinese University of Hong Kong, Shenzhen

Helmut Bölcskei ETH Zurich

Gitta Kutyniok Ludwig-Maximilians-Universität München

Christoph Schwab ETH Zurich

Ingrid Daubechies Duke University

Helmut Pottmann TU Wien

Demetrio Labate University of Houston

Stephan Dahlke Philipp University of Marburg

Ralf Hiptmair ETH Zurich

Afra M. Wohlschläger Technical University of Munich

External Links

Personal website of Philipp Grohs

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