  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
ordinary differential equations, 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 with important benchmark
problems from computational physics.
