1. Stochastic gradient descent with noise of machine learning type. Part I: Discrete time analysis
    2021 ArXiv
  2. A priori estimates for classification problems using neural networks
    (with Weinan E) 2020 ArXiv
  3. Representation Formulas and Pointwise Properties for Barron Functions
    (with Weinan E) 2020 ArXiv
  4. On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime
    2020 ArXiv
  5. Connected Coulomb Columns: Analysis and Numerics
    (with P. Dondl, M. Novaga and S. Wolff-Vorbeck), 2018 ArXiv
  6. Keeping it together: a phase field version of path-connectedness and its implementation
    (with P. Dondl), 2018 ArXiv

Published and accepted articles

  1. On the emergence of tetrahedral symmetry in the final and penultimate layers of neural network classifiers
    (with Weinan E) 2020 ArXiv
  2. Some observations on partial differential equations in Barron and multi-layer spaces
    (with Weinan E) 2020 ArXiv
  3. Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't
    (with Weinan E, Chao Ma and Lei Wu) 2020 Journal ArXiv
  4. On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics
    (with Weinan E) 2020 Journal ArXiv
  5. The motion of curved dislocations in three dimensions: Simplified linearized elasticity
    (with I. Fonseca and J. Ginster), 2020 Journal ArXiv
  6. Can shallow neural networks beat the curse of dimensionality? A mean field training perspective
    (with Weinan E), 2020 Journal ArXiv
  7. Kolmogorov Width Decay and Poor Approximators in Machine Learning: Shallow Neural Networks, Random Feature Models and Neural Tangent Kernels
    (with Weinan E), Res Math Sci, 2020 Journal ArXiv
  8. Confined elasticae and the buckling of cylindrical shells
    Adv Calc Var (2020) Journal ArXiv
  9. Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields
    (with P. Dondl, M. Novaga and B. Wirth), SIAM Journal on Mathematical Analysis (2019) 51:5 Journal ArXiv
  10. The Effect of Forest Dislocations on the Evolution of a Phase-Field Model for Crystal Dislocations
    (with P. Dondl and M. Kurzke), Arch Rational Mech Anal (2018) 232 Journal ArXiv
  11. Phase Field Models for Thin Elastic Structures with Topological Constraint
    (with P. Dondl and A. Lemenant), Arch Rational Mech Anal (2017) 223 Journal ArXiv
  12. Uniform Regularity and Convergence of Phase Fields for Willmore's Energy
    (with P. Dondl), Calc. Var. PDE (2017) 56 Journal ArXiv 
  13. On the Boundary Regularity of Phase-Fields for Willmore's Energy
    (with P. Dondl), Proc A Royal Soc of Edinburgh (2017) 149:4 Journal ArXiv
  14. Helfrich's Energy and Constrained Minimisation
    Comm in Math Sci (2017) 15:8 Journal ArXiv 
  15. On the Alexandrov Topology of Sub-Lorentzian Manifolds
    (with I. Markina), Geometric Control Theory and Sub-Riemannian Geometry, Springer INdAM Series (2014) Book ArXiv
You can also find my publications on Orcid and ArXiv. Some publications are also available on cvgmt or DeepAI respectively.

last updated May 2021