philipp grohs
Optimal approximation with sparsely connected deep neural networks
H Bolcskei, P Grohs, G Kutyniok, P Petersen
SIAM Journal on Mathematics of Data Science 1 (1), 8-45, 2019
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
P Grohs, F Hornung, A Jentzen, P Von Wurstemberger
Memoirs of the American Mathematical Society, 2018
Deep neural network approximation theory
D Elbrächter, D Perekrestenko, P Grohs, H Bölcskei
IEEE Transactions on Information Theory, 2019
The modern mathematics of deep learning
J Berner, P Grohs, G Kutyniok, P Petersen
arXiv preprint arXiv:2105.04026 78, 2021
Solving the Kolmogorov PDE by means of deep learning
C Beck, S Becker, P Grohs, N Jaafari, A Jentzen
Journal of Scientific Computing 88, 1-28, 2021
Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of …
J Berner, P Grohs, A Jentzen
SIAM Journal on Mathematics of Data Science 2 (3), 631-657, 2020
DNN expression rate analysis of high-dimensional PDEs: application to option pricing
D Elbrächter, P Grohs, A Jentzen, C Schwab
Constructive Approximation 55 (1), 3-71, 2022
Laguerre minimal surfaces, isotropic geometry and linear elasticity
H Pottmann, P Grohs, NJ Mitra
Advances in computational mathematics 31 (4), 391, 2009
Parabolic molecules
P Grohs, G Kutyniok
Foundations of Computational Mathematics 14, 299-337, 2014
Phase retrieval: uniqueness and stability
P Grohs, S Koppensteiner, M Rathmair
SIAM Review 62 (2), 301-350, 2020
ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds
P Grohs, S Hosseini
Advances in Computational Mathematics 42, 333-360, 2016
Stable phase retrieval in infinite dimensions
R Alaifari, I Daubechies, P Grohs, R Yin
Foundations of Computational Mathematics 19, 869-900, 2019
Continuous shearlet frames and resolution of the wavefront set
P Grohs
Monatshefte für Mathematik 164 (4), 393-426, 2011
Phase retrieval in the general setting of continuous frames for Banach spaces
R Alaifari, P Grohs
SIAM journal on mathematical analysis 49 (3), 1895-1911, 2017
Group testing for SARS-CoV-2 allows for up to 10-fold efficiency increase across realistic scenarios and testing strategies
CM Verdun, T Fuchs, P Harar, D Elbrächter, DS Fischer, J Berner, ...
Frontiers in Public Health 9, 583377, 2021
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions
P Grohs, L Herrmann
IMA Journal of Numerical Analysis 42 (3), 2055-2082, 2022
Stable Gabor phase retrieval and spectral clustering
P Grohs, M Rathmair
Communications on Pure and Applied Mathematics 72 (5), 981-1043, 2019
Space-time error estimates for deep neural network approximations for differential equations
P Grohs, F Hornung, A Jentzen, P Zimmermann
Advances in Computational Mathematics 49 (1), 4, 2023
Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks
M Scherbela, R Reisenhofer, L Gerard, P Marquetand, P Grohs
Nature Computational Science 2 (5), 331-341, 2022
Numerically solving parametric families of high-dimensional Kolmogorov partial differential equations via deep learning
J Berner, M Dablander, P Grohs
Advances in Neural Information Processing Systems 33, 16615-16627, 2020
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