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We present a data-driven, space-time continuous framework to learn surrogatemodels for complex physical systems described by advection-dominated partialdifferential equations. Those systems have slow-decaying Kolmogorov n-widththat hinders standard methods, including reduced order modeling, from producinghigh-fidelity simulations at low cost. In this work, we constructhypernetwork-based latent dynamical models directly on the parameter space of acompact representation network. We leverage the expressive power of the networkand a specially designed consistency-inducing regularization to obtain latenttrajectories that are both low-dimensional and smooth. These properties renderour surrogate models highly efficient at inference time. We show the efficacyof our framework by learning models that generate accurate multi-step rolloutpredictions at much faster inference speed compared to competitors, for severalchallenging examples.

Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems