We study the performance of long short-term memory networks (LSTMs) and neural ordinary
differential equations (NODEs) in learning latent-space representations of dynamical
equations for an advection-dominated problem given by the viscous Burgers equation. Our
formulation is devised in a nonintrusive manner with an equation-free evolution of dynamics
in a reduced space with the latter being obtained through a proper orthogonal
decomposition. In addition, we leverage the sequential nature of learning for both LSTMs …