Invariant Foliations for Data-Driven Reduced Order Modelling

Invariant foliations are the only mathematical structure that are guaranteed to produce both invariant and unique reduced order models from data. Following on from initial investigations, in this talk we demonstrate how invariant foliations are used to identify reduced order models about invariant tori in (quasi-) periodically forced systems. We show that invariant foliations both exist and unique under some non-resonance conditions for real analytic dynamical systems. The examples include video data from a forced clamped-clamped plate experiment, a traffic model and the vibrations of the London Millenium bridge under pedestrian flow.