Graphical Models and Belief Propagation-hierarchy for Optimal Physics-Constrained Network Flows

TL;DR

This paper reviews the application of graphical models, inspired by physics and information theory, to optimize physics-constrained network flows in large-scale power and gas systems, highlighting new ideas and initial results.

Contribution

It introduces a novel approach combining graphical models with physics constraints for optimizing large-scale network flows, with practical examples from power and gas networks.

Findings

Demonstrates the effectiveness of graphical models in complex network flow optimization

Provides initial results on power and gas transmission systems

Highlights potential for physics-informed optimization methods

Abstract

In this manuscript we review new ideas and first results on application of the Graphical Models approach, originated from Statistical Physics, Information Theory, Computer Science and Machine Learning, to optimization problems of network flow type with additional constraints related to the physics of the flow. We illustrate the general concepts on a number of enabling examples from power system and natural gas transmission (continental scale) and distribution (district scale) systems.