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A state variable is a coordinate used to describe the instantaneous condition of a dynamical system sufficiently completely to determine its future evolution under a specified model and input. For a simple pendulum, its angle and angular velocity form a state; angle alone generally does not, because the same position can be traversed in either direction.

A second-order ordinary differential equation $\ddot{q}=f(q,\dot{q},t)$ becomes a first-order system by setting $v=\dot{q}$: $\dot{q}=v$ and $\dot{v}=f(q,v,t)$. The choice of state variables therefore reflects the memory required by the model, and differs from merely listing measured outputs.

Yannis G. Kevrekidis is a chemical engineer whose research connects dynamical systems, multiscale modeling and machine learning. His institutional research description emphasizes how interactions at small scales produce larger-scale patterns, instabilities and dynamics in physical, chemical and biological systems.^[ref]

With collaborators he developed equation-free modeling, in which detailed simulations are used to investigate coarse-scale behaviour even when a closed equation for the coarse variables is unavailable. The motivating distinction is between possessing a simulator of microscopic dynamics and possessing a compact equation for a few large-scale observables. This places numerical analysis, the choice of state variables and the extraction of useful descriptions at the centre of multiscale modeling.^[ref]