Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems
This work addresses the problem of computationally expensive simulations for researchers and engineers in computational physics, though it appears incremental as it builds on existing latent modeling approaches with specific regularization.
The paper tackles the challenge of creating efficient surrogate models for advection-dominated physical systems, which are difficult to simulate due to slow-decaying Kolmogorov n-width, by developing a hypernetwork-based latent dynamical framework that achieves accurate multi-step rollout predictions with much faster inference speed compared to competitors.
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.