  We present a data-driven, space-time continuous framework to learn surrogate
models for complex physical systems described by advection-dominated partial
differential equations. Those systems have slow-decaying Kolmogorov n-width
that hinders standard methods, including reduced order modeling, from producing
high-fidelity simulations at low cost. In this work, we construct
hypernetwork-based latent dynamical models directly on the parameter space of a
compact representation network. We leverage the expressive power of the network
and a specially designed consistency-inducing regularization to obtain latent
trajectories that are both low-dimensional and smooth. These properties render
our surrogate models highly efficient at inference time. We show the efficacy
of our framework by learning models that generate accurate multi-step rollout
predictions at much faster inference speed compared to competitors, for several
challenging examples.
