Probabilistic Behavioral Distance and Tuning - Reducing and aggregating complex systems

TL;DR

This paper introduces probabilistic behavioral distances to quantify how closely complex systems match simpler specifications, enabling effective tuning and aggregation of large networks, with potential applications in model reduction.

Contribution

It proposes new probabilistic behavioral distance measures and demonstrates their use in tuning and aggregating complex systems, including networked systems.

Findings

Successfully tuned non-linear networked systems to smaller networks

Enabled aggregation of large sub-networks into fewer effective nodes

Discussed relation to $H_ fty$ model reduction

Abstract

Given a complex system with a given interface to the rest of the world, what does it mean for a the system to behave close to a simpler specification describing the behavior at the interface? We give several definitions for useful notions of distances between a complex system and a specification by combining a behavioral and probabilistic perspective. These distances can be used to tune a complex system to a specification. We show that our approach can successfully tune non-linear networked systems to behave like much smaller networks, allowing us to aggregate large sub-networks into one or two effective nodes. Finally, we discuss similarities and differences between our approach and $H_\infty$ model reduction.