A slime mold inspired local adaptive mechanism for flow networks

TL;DR

This paper introduces a biologically inspired local adaptive mechanism for flow networks, enabling dynamic optimization based on local information, with demonstrated scalability and phase transition analysis.

Contribution

It presents a novel physical mechanism inspired by slime mold that allows flow networks to adapt locally for global optimization, including phase diagram analysis.

Findings

Mechanism is scalable to larger networks

Identifies phase boundary for successful adaptation

Reveals a SAT-UNSAT phase transition in network tuning

Abstract

In the realm of biological flow networks, the ability to dynamically adjust to varying demands is paramount. Drawing inspiration from the remarkable adaptability of Physarum polycephalum, we present a novel physical mechanism tailored to optimize flow networks. Central to our approach is the principle that each network component -- specifically, the tubes -- harnesses locally available information to collectively minimize a global cost function. Our findings underscore the scalability of this mechanism, making it feasible for larger, more complex networks. We construct a comprehensive phase diagram, pinpointing the specific network parameters under which successful adaptation, or tuning, is realized. There exists a phase boundary in the phase diagram, revealing a distinct satisfiability-unsatisfiability (SAT-UNSAT) phase transition delineating successful and unsuccessful adaptation.