Inherent limits on optimization and discovery in physical systems

TL;DR

This paper investigates the fundamental limitations in optimizing and understanding physical systems through topological mapping and motif-based representations, revealing inherent constraints on system reconstruction and optimization potential.

Contribution

It introduces a framework for topological mapping and decomposition of physical systems, highlighting inherent limits to optimization and reconstruction from approximate representations.

Findings

Different representations optimize and describe systems best

Inherent limits restrict system reconstruction accuracy

Motif-based approximations may not fully capture system complexity

Abstract

Topological mapping of a large physical system on a graph, and its decomposition using universal measures is proposed. We find inherent limits to the potential for optimization of a given system and its approximate representations by motifs, and the ability to reconstruct the full system given approximate representations. The approximate representation of the system most suited for optimization may be different from that which most accurately describes the full system.