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Equation-free modeling performs coarse-scale calculations using short runs of a finer-scale simulator when an explicit coarse evolution equation is unavailable. A lifting step constructs microscopic states consistent with coarse variables; simulation advances them; restriction measures the resulting coarse state. These operations define a coarse time-stepper. ^[ref]

For example, microscopic cell states can be initialized to match a population density, evolved briefly, and averaged to estimate a coarse change rate. That estimate can feed a longer projective step or a steady-state calculation. The method needs suitable coarse variables and separation between fast relaxation and slow evolution. If unresolved memory remains important, two microscopic preparations with the same coarse value can evolve differently, invalidating the assumed closure.

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]