Neural Latent Dynamics Models

Nicola Farenga, Stefania Fresca, Andrea Manzoni

Keywords: Latent Dynamics Learning, Model Discovery, Neural ODEs, Reduced Order Modeling, Parameterized PDEs

Abstract: We introduce Neural Latent Dynamics Models (NLDMs), a neural ordinary differential equations (ODEs)-based architecture to perform end-to-end nonlinear latent dynamics discovery, without the need to include any inductive bias related to either the underlying physical model or the latent coordinates space. The effectiveness of this strategy is experimentally tested in the framework of reduced order modeling, considering a set of problems involving high-dimensional data generated from nonlinear time-dependent parameterized partial differential equations (PDEs) simulations, where we aim at performing extrapolation in time, to forecast the PDE solution out of the time interval and/or the parameters range where training data were acquired. Results highlight NLDMs' capabilities to perform low-dimensional latent dynamics learning in three different scenarios.