The purpose of this research is to provide ground-breaking advances in the simplification of models directly from data (data-driven model order reduction) for the classes of time-varying, of nonlinear, and of multidimensional dynamical systems. Time-varying and nonlinear phenomena are predominant in physics and engineering (e.g. in MEMS, VLSI circuits, smart grids, robotics, automotive and aerospace engineering, molecular biology, to name but a
few), and consequently this research will have wide application in several areas.

The usual approach to model order reduction consists in postulating a set of equations containing unspecified parameters that are to be fitted to the data. The nature and quantity of the equation parameters is determined by insight into the model, or by assumptions that are mathematically instrumental to achieve some explanation for the measurements. The conceptual foundation of the research proposed here is instead to let the data speak for
itself. We aim to provide (reduced-order) modelling procedures that starting from the smallest possible set of assumptions on the system, directly construct mathematical models for it. In fact, the only postulate made about the system is that a balance relation exists among the system variables, involving the measured quantities (e.g. inputs and outputs) and the state of the system.