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SUMMARY:Second Order Behaviour in Augmented Neural ODEs - Alexander Norcli
 ffe
DTSTART:20201110T131500Z
DTEND:20201110T141500Z
UID:TALK152935@talks.cam.ac.uk
CONTACT:Mateja Jamnik
DESCRIPTION:"Join us on Zoom":https://zoom.us/j/99166955895?pwd=SzI0M3pMVE
 kvNmw3Q0dqNDVRalZvdz09\n\nNeural Ordinary Differential Equations (NODEs) a
 re a new class of models that transform data continuously through infinite
 -depth architectures. The continuous nature of NODEs has made them particu
 larly suitable for learning the dynamics of complex physical systems. Whil
 e previous work has mostly been focused on first order ODEs\, the dynamics
  of many systems\, especially in classical physics\, are governed by secon
 d order laws. In this work\, we consider Second Order Neural ODEs (SONODEs
 ). We show how the adjoint sensitivity method can be extended to SONODEs a
 nd prove that the optimisation of a first order coupled ODE is equivalent 
 and computationally more efficient. Furthermore\, we extend the theoretica
 l understanding of the broader class of Augmented NODEs (ANODEs) by showin
 g they can also learn higher order dynamics with a minimal number of augme
 nted dimensions\, but at the cost of interpretability. This indicates that
  the advantages of ANODEs go beyond the extra space offered by the augment
 ed dimensions\, as originally thought. Finally\, we compare SONODEs and AN
 ODEs on synthetic and real dynamical systems and demonstrate that the indu
 ctive biases of the former generally result in faster training and better 
 performance.\n\n"arXiv":https://arxiv.org/abs/2006.07220\n\n"NeurIPS pre-p
 roceedings":https://papers.nips.cc/paper/2020/hash/418db2ea5d227a9ea8db8e5
 357ca2084-Abstract.html
LOCATION:Zoom
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