Optimal high-level descriptions of dynamical systems

Understand

To analyze high-dimensional systems, many fields in science and engineering rely on high-level descriptions, sometimes called "macrostates," "coarse-grainings," or "effective theories".

• Examples of such descriptions include the thermodynamic properties of a large collection of point particles undergoing reversible dynamics, the variables in a macroeconomic model describing the individuals that participate in an economy, and the summary state of a cell composed of a large set of biochemical networks.
• Often these high-level descriptions are constructed without considering the ultimate reason for needing them in the first place.
• Here, we formalize and quantify one such purpose: the need to predict observables of interest concerning the high-dimensional system with as high accuracy as possible, while minimizing the computational cost of doing so.