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 | 54 | 2020 |

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 | 49 | 2020 |

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 | 36 | 2022 |

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 | 26 | 2017 |

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 | 20 | 2023 |

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 | 10 | 2016 |

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 | 8 | 2021 |

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 | 8 | 2019 |

Stochastic gradient descent with noise of machine learning type part II: Continuous time analysis S Wojtowytsch Journal of Nonlinear Science 34 (1), 16, 2024 | 6 | 2024 |

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 | 6 | 2019 |

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 | 6 | 2017 |

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 | 5 | 2021 |

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 | 4 | 2018 |