### Abstract

The engineering design process often relies on mathematical models to describe dynamic behavior. In this talk, we discuss a data-driven methodology for modeling nonlinear systems dynamics by identifying coordinate transformation that represent these dynamics using a simple, common model structure. This common model structure allows for the application of specialised design tools across a wide range of nonlinear systems. Linear models are the simplest models but are not able capture complex nonlinear dynamics in a finite dimensional space. Therefore, we discuss using quadratic systems as the common structure, inspired by the lifting principle. The principle suggests that smooth nonlinear systems can be represented as quadratic systems in appropriate coordinates. In a data-driven setting, we aim to learn such a coordinate system using neural networks. Moreover, many physical processes are asymptotic stable. In this case, we also discuss how to enforce asymptotic stability for the learned coordinates. Furthermore, we also present an extension to canonical Hamiltonian systems. Several numerical examples are presented to illustrate the methodology.