Follow
Stephan Wojtowytsch
Title
Cited by
Cited by
Year
Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't
W E, C Ma, S Wojtowytsch, L Wu
arXiv preprint arXiv:2009.10713, 2020
115*2020
Stochastic gradient descent with noise of machine learning type. Part I: Discrete time analysis
S Wojtowytsch
arXiv preprint arXiv:2105.01650, 2021
67*2021
On the convergence of gradient descent training for two-layer ReLU-networks in the mean field regime
S Wojtowytsch
arXiv preprint arXiv:2005.13530, 2020
542020
Can shallow neural networks beat the curse of dimensionality? A mean field training perspective
S Wojtowytsch, W E
IEEE Transactions on Artificial Intelligence 1 (2), 121-129, 2020
492020
On the emergence of simplex symmetry in the final and penultimate layers of neural network classifiers
E Weinan, S Wojtowytsch
Mathematical and Scientific Machine Learning, 270-290, 2022
46*2022
On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics
W E, S Wojtowytsch
arXiv preprint arXiv:2007.15623 8, 2020
44*2020
Representation formulas and pointwise properties for Barron functions
E Weinan, S Wojtowytsch
Calculus of Variations and Partial Differential Equations 61 (2), 46, 2022
362022
Some observations on high-dimensional partial differential equations with Barron data
W E, S Wojtowytsch
arXiv preprint arXiv:2012.01484, 2020
28*2020
Phase field models for thin elastic structures with topological constraint
PW Dondl, A Lemenant, S Wojtowytsch
Archive for Rational Mechanics and Analysis 223 (2), 693-736, 2017
262017
Group equivariant fourier neural operators for partial differential equations
J Helwig, X Zhang, C Fu, J Kurtin, S Wojtowytsch, S Ji
arXiv preprint arXiv:2306.05697, 2023
202023
Kolmogorov width decay and poor approximators in machine learning: Shallow neural networks, random feature models and neural tangent kernels
W E, S Wojtowytsch
Research in the Mathematical Sciences 8 (1), 1-28, 2021
18*2021
Representation formulas and pointwise properties for Barron functions
W E, S Wojtowytsch
Calculus of Variations and Partial Differential Equations 61 (2), 1-37, 2022
15*2022
Helfrich's Energy and Constrained Minimisation
S Wojtowytsch
arXiv preprint arXiv:1608.02823, 2016
102016
Keeping it together: A phase-field version of path-connectedness and its implementation
P Dondl, S Wojtowytsch
Journal of Algorithms & Computational Technology 15, 17483026211054342, 2021
82021
The effect of forest dislocations on the evolution of a phase-field model for plastic slip
PW Dondl, MW Kurzke, S Wojtowytsch
Archive for Rational Mechanics and Analysis 232 (1), 65-119, 2019
82019
Stochastic gradient descent with noise of machine learning type part II: Continuous time analysis
S Wojtowytsch
Journal of Nonlinear Science 34 (1), 16, 2024
62024
A phase-field approximation of the perimeter under a connectedness constraint
PW Dondl, M Novaga, B Wirth, S Wojtowytsch
SIAM Journal on Mathematical Analysis 51 (5), 3902-3920, 2019
62019
Uniform regularity and convergence of phase-fields for Willmore’s energy
PW Dondl, S Wojtowytsch
Calculus of Variations and Partial Differential Equations 56 (4), 90, 2017
62017
On the motion of curved dislocations in three dimensions: simplified linearized elasticity
I Fonseca, J Ginster, S Wojtowytsch
SIAM Journal on Mathematical Analysis 53 (2), 2373-2426, 2021
52021
Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields
P Dondl, M Novaga, B Wirth, S Wojtowytsch
arXiv preprint arXiv:1810.05787, 2018
42018
The system can't perform the operation now. Try again later.
Articles 1–20