• Deep learning as optimal control problems: models and numerical methods 

      Benning, Martin; Celledoni, Elena; Ehrhardt, Matthias J.; Owren, Brynjulf; Schönlieb, Carola-Bibiane (Journal article; Peer reviewed, 2019)
      We consider recent work of [11] and [6], where deep learning neuralnetworks have been interpreted as discretisations of an optimal control problemsubject to an ordinary differential equation constraint. We review the first ...
    • Equivariant neural networks for inverse problems 

      Celledoni, Elena; Ehrhardt, Matthias J.; Etmann, Christian; Owren, Brynjulf; Schönlieb, Carola-Bibiane; Sherry, Ferdia (Peer reviewed; Journal article, 2021)
      In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of ...
    • Structure preserving neural networks based on ODEs 

      Murari, Davide; Celledoni, Elena; Owren, Brynjulf Rustad; Sherry, Ferdia; Schönlieb, Carola-Bibiane (Research report, 2022)
    • Variational image regularization with Euler's elastica using a discrete gradient scheme 

      Ringholm, Torbjørn; Lazic, Jasmina; Schönlieb, Carola-Bibiane (Journal article; Peer reviewed, 2018)
      This paper concerns an optimization algorithm for unconstrained nonconvex problems where the objective function has sparse connections between the unknowns. The algorithm is based on applying a dissipation preserving ...