On latent dynamics learning in nonlinear reduced order modeling

Nicola Farenga, Stefania Fresca, Simone Brivio, Andrea Manzoni

Abstract: Highlights•Dimensionality reduction framework preserving the structure of dynamical systems.•Key properties of LDMs: causality, IVP structure and time-resolution invariance.•Connection between abstract and learnable settings unlocking time-continuity.•Implementation with spatially-coherent autoencoders and parameterized Neural ODEs.•Applications involving (nonlinear) Burgers’ equation and (non-affine) ADR equation.