Deep learning as optimal control problems

Martin Benning, Elena Celledoni, Matthias J. Ehrhardt, Brynjulf Owren, Carola Bibiane Schonlieb

Research output: Contribution to journalConference articlepeer-review

2 Citations (SciVal)


We briefly review recent work where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We report here new preliminary experiments with implicit symplectic Runge-Kutta methods. In this paper, we discuss ongoing and future research in this area.

Original languageEnglish
Pages (from-to)620-623
Number of pages4
Issue number9
Early online date16 Jul 2021
Publication statusPublished - 31 Dec 2021
Event24th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2020 - Cambridge, UK United Kingdom
Duration: 23 Aug 202127 Aug 2021


  • Deep neural networks
  • Optimal control
  • Resnet

ASJC Scopus subject areas

  • Control and Systems Engineering


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