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

• URL: http://arxiv.org/abs/2301.10391v2
• Date: Thu, 26 Jan 2023 01:32:45 GMT
• Title: Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems
• Authors: Zhong Yi Wan, Leonardo Zepeda-N\'u\~nez, Anudhyan Boral and Fei Sha
• Abstract summary: We present a data-driven, space-time continuous framework to learn surrogatemodels for complex physical systems. We leverage the expressive power of the network and aspecially designed consistency-inducing regularization to obtain latent trajectories that are both low-dimensional and smooth.
• Score: 14.553972457854517
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 Kolmogorovn-widththat hinders standard methods, including reduced order modeling, from producinghigh-fidelity simulations at low cost. In this work, we construct hypernetwork-based latent dynamical models directly on the parameter space of a compactrepresentation network. We leverage the expressive power of the network and aspecially designed consistency-inducing regularization to obtain latent trajectoriesthat are both low-dimensional and smooth. These properties render our surrogatemodels highly efficient at inference time. We show the efficacy of our frameworkby learning models that generate accurate multi-step rollout predictions at muchfaster inference speed compared to competitors, for several challenging examples.

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