Machine-learning invariant foliations in forced systems for reduced order modelling

arXiv:2403.14514v1 Announce Type: cross
Abstract: We identify reduced order models (ROM) of forced systems from data using invariant foliations. The forcing can be external, parametric, periodic or quasi-periodic. The process has four steps: 1. identify an approximate invariant torus and the linear dynamics about the torus; 2. identify a globally defined invariant foliation about the torus; 3. identify a local foliation about an invariant manifold that complements the global foliation 4. extract the invariant manifold as the leaf going through …

abstract arxiv cs.lg data dynamics identify linear machine math.ds modelling parametric process systems type