This chapter presents a rigorous method for calibrating an Ideal Flow Network (IFN) by leveraging the Principle of Maximum Entropy (MEP). It establishes that traditional network-wide entropy metrics are insufficient, and proposes a more granular approach; a flow-weighted average of node entropies. This metric quantifies the uncertainty of flow distribution at a microscopic level. The chapter demonstrates that calibrating an IFN is an inverse problem solvable through a constrained optimization framework where network entropy is maximized. This methodology provides a logical and robust solution to the common problem of incomplete data in real-world networks, enabling the estimation of a maximally unbiased flow matrix. The concepts are illustrated with both theoretical proofs and practical examples, bridging the gap between abstract theory and real-world application.

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The Principle of Maximum Entropy in IFN Estimation

  • Kardi Teknomo

摘要

This chapter presents a rigorous method for calibrating an Ideal Flow Network (IFN) by leveraging the Principle of Maximum Entropy (MEP). It establishes that traditional network-wide entropy metrics are insufficient, and proposes a more granular approach; a flow-weighted average of node entropies. This metric quantifies the uncertainty of flow distribution at a microscopic level. The chapter demonstrates that calibrating an IFN is an inverse problem solvable through a constrained optimization framework where network entropy is maximized. This methodology provides a logical and robust solution to the common problem of incomplete data in real-world networks, enabling the estimation of a maximally unbiased flow matrix. The concepts are illustrated with both theoretical proofs and practical examples, bridging the gap between abstract theory and real-world application.