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Maximum Entropy Analysis of Flow Networks: Theoretical Foundation and Applications

1
School of Engineering and Information Technology, The University of New South Wales, Northcott Drive, Canberra, ACT 2600, Australia
2
Ambrosys GmbH, 14469 Potsdam, Germany
3
Institute for Physics and Astrophysics, University of Potsdam, 14469 Potsdam, Germany
4
Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, 10623 Berlin, Germany
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(8), 776; https://doi.org/10.3390/e21080776
Received: 24 June 2019 / Revised: 29 July 2019 / Accepted: 31 July 2019 / Published: 8 August 2019
(This article belongs to the Special Issue Entropy Based Inference and Optimization in Machine Learning)
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Abstract

The concept of a “flow network”—a set of nodes and links which carries one or more flows—unites many different disciplines, including pipe flow, fluid flow, electrical, chemical reaction, ecological, epidemiological, neurological, communications, transportation, financial, economic and human social networks. This Feature Paper presents a generalized maximum entropy framework to infer the state of a flow network, including its flow rates and other properties, in probabilistic form. In this method, the network uncertainty is represented by a joint probability function over its unknowns, subject to all that is known. This gives a relative entropy function which is maximized, subject to the constraints, to determine the most probable or most representative state of the network. The constraints can include “observable” constraints on various parameters, “physical” constraints such as conservation laws and frictional properties, and “graphical” constraints arising from uncertainty in the network structure itself. Since the method is probabilistic, it enables the prediction of network properties when there is insufficient information to obtain a deterministic solution. The derived framework can incorporate nonlinear constraints or nonlinear interdependencies between variables, at the cost of requiring numerical solution. The theoretical foundations of the method are first presented, followed by its application to a variety of flow networks. View Full-Text
Keywords: maximum entropy analysis; flow network; probabilistic inference maximum entropy analysis; flow network; probabilistic inference
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Niven, R.K.; Abel, M.; Schlegel, M.; Waldrip, S.H. Maximum Entropy Analysis of Flow Networks: Theoretical Foundation and Applications. Entropy 2019, 21, 776.

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