Hierarchical deep learning for data-driven identification of reduced-order models of nonlinear dynamical systems

Identifying reduced-order models (ROMs) of nonlinear dynamical systems is difficult, especially when the system equation is unknown with only measurement data available. In such a case, not only a reduced subspace but also the associated dynamics need to be identified from data only, leading to a challenging data-driven ROM problem. In this study, we present a hierarchical deep learning approach to identify ROM from measurement only; it simultaneously identifies the nonlinear normal modal (NNM) subspace with a hierarchical order and the associated nonlinear modal dynamics. We conduct study to validate such an approach on both unforced and forced nonlinear dynamical systems, and find that the identified hierarchical NNMs-spanned subspace enables an efficient and effective dimensional truncation to achieve optimally lowest-dimensional ROM. We discuss in detail its performance and applicability.