• Structure preserving deep learning 

      Celledoni, Elena; Ehrhardt, Matthias J.; Etmann, Christian; McLachlan, Robert I.; Owren, Brynjulf; Schönlieb, Carola-Bibiane; Sherry, Ferdia (Peer reviewed; Journal article, 2021)
      Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging ...
    • Symplectic integration of PDEs using Clebsch variables 

      McLachlan, Robert I.; Offen, Christian; Tapley, Benjamin (Journal article, 2019)
      Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations, …) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The ...
    • Using aromas to search for preserved measures and integrals in Kahan’s method 

      Bogfjellmo, Geir; Celledoni, Elena; McLachlan, Robert I.; Owren, Brynjulf Rustad; Quispel, Gilles Reinout Willem (Peer reviewed; Journal article, 2023)
      The numerical method of Kahan applied to quadratic differential equations is known to often generate integrable maps in low dimensions and can in more general situations exhibit preserved measures and integrals. Computerized ...