Parameterized neural ordinary differential equations: Applications to computational physics problems

Kookjin Lee, Eric J. Parish

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter instances. Our extension is inspired by the concept of parameterized ODEs, which are widely investigated in computational science and engineering contexts, where characteristics of the governing equations vary over the input parameters. We apply the proposed parameterized NODEs (PNODEs) for learning latent dynamics of complex dynamical processes that arise in computational physics, which is an essential component for enabling rapid numerical simulations for time-critical physics applications. For this, we propose an encoder-decoder-type framework, which models latent dynamics as PNODEs. We demonstrate the effectiveness of PNODEs on benchmark problems from computational physics.

Original languageEnglish (US)
Article number20210162
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2253
StatePublished - 2021


  • autoencoders
  • deep learning
  • latent-dynamics learning
  • model reduction
  • neural ordinary differential equations
  • nonlinear manifolds

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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