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philipp grohs
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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
2202019
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
1612018
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
1352020
Deep neural network approximation theory
D Elbrächter, D Perekrestenko, P Grohs, H Bölcskei
IEEE Transactions on Information Theory, 2019
1332019
Solving the Kolmogorov PDE by means of deep learning
C Beck, S Becker, P Grohs, N Jaafari, A Jentzen
Journal of Scientific Computing 88 (3), 1-28, 2021
1292021
Laguerre minimal surfaces, isotropic geometry and linear elasticity
H Pottmann, P Grohs, NJ Mitra
Advances in computational mathematics 31 (4), 391-419, 2009
872009
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
832022
Parabolic molecules
P Grohs, G Kutyniok
Foundations of Computational Mathematics 14 (2), 299-337, 2014
832014
Continuous shearlet frames and resolution of the wavefront set
P Grohs
Monatshefte für Mathematik 164 (4), 393-426, 2011
662011
Stable phase retrieval in infinite dimensions
R Alaifari, I Daubechies, P Grohs, R Yin
Foundations of Computational Mathematics 19 (4), 869-900, 2019
582019
ε-subgradient algorithms for locally Lipschitz functions on Riemannian manifolds
P Grohs, S Hosseini
Advances in Computational Mathematics 42 (2), 333-360, 2016
522016
Smoothness properties of Lie group subdivision schemes
J Wallner, EN Yazdani, P Grohs
Multiscale modeling & simulation 6 (2), 493-505, 2007
492007
Phase retrieval: uniqueness and stability
P Grohs, S Koppensteiner, M Rathmair
SIAM Review 62 (2), 301-350, 2020
452020
A general proximity analysis of nonlinear subdivision schemes
P Grohs
SIAM Journal on Mathematical Analysis 42 (2), 729-750, 2010
452010
The modern mathematics of deep learning
J Berner, P Grohs, G Kutyniok, P Petersen
arXiv preprint arXiv:2105.04026, 2021
442021
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
432017
Optimal a priori discretization error bounds for geodesic finite elements
P Grohs, H Hardering, O Sander
Foundations of Computational Mathematics 15 (6), 1357-1411, 2015
422015
Stable Gabor phase retrieval and spectral clustering
P Grohs, M Rathmair
Communications on Pure and Applied Mathematics 72 (5), 981-1043, 2019
402019
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, 1205, 2021
382021
Interpolatory wavelets for manifold-valued data
P Grohs, J Wallner
Applied and Computational Harmonic Analysis 27 (3), 325-333, 2009
372009
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Articles 1–20