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Towards a Tensor Network Representation of Complex Systems

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Sustainable Interdependent Networks II

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 186))

Abstract

Complex networks are composed of nodes (entities) and edges (connections) with any arbitrary topology. There may also exist multiple types of interactions among these nodes and each node may admit different states in each of its interactions with its neighbors. Understanding complex networks dwells on understanding their structure and function. However, current representations model nodes as single-state entities that are connected to each other differently and treat their dynamics separately with some differential equations. Alternatively, a unified framework might be accessible using the tensor network representation that is already utilized in physics communities. In a sequel of chapters we introduce tensor network representation and renormalization as an alternative framework to explore the universal behaviors of complex systems. We hope that tensor networks can particularly pave the way for better understanding of the sustainable interdependent networks (Amini et al., Sustainable interdependent networks: from theory to application, 2018) through proposing efficient computational strategies and discovering insightful features of the network behaviors.

“It is not the strongest of the species that survives, nor the most intelligent, but the one most responsive to change.”

Charles Darwin (1809)

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA, USA

    Pouria Mistani, Samira Pakravan & Frederic Gibou

  2. Department of Computer Science, University of California Santa Barbara, Santa Barbara, CA, USA

    Frederic Gibou

Authors
  1. Pouria Mistani
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  2. Samira Pakravan
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  3. Frederic Gibou
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Corresponding author

Correspondence to Pouria Mistani .

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, USA

    M. Hadi Amini

  2. School of Computing and Information Sciences, Florida International University, Miami, FL, USA

    Kianoosh G. Boroojeni

  3. School of Computing and Information Sciences, Florida International University, Miami, FL, USA

    S. S. Iyengar

  4. Department of Industrial & Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  5. Department of Energy Technology, Aalborg University, Aalborg, Denmark

    Frede Blaabjerg

  6. Department of Electrical & Computer Engineering, University of California Los Angeles, Los Angeles, CA, USA

    Asad M. Madni

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Mistani, P., Pakravan, S., Gibou, F. (2019). Towards a Tensor Network Representation of Complex Systems. In: Amini, M., Boroojeni, K., Iyengar, S., Pardalos, P., Blaabjerg, F., Madni, A. (eds) Sustainable Interdependent Networks II. Studies in Systems, Decision and Control, vol 186. Springer, Cham. https://doi.org/10.1007/978-3-319-98923-5_4

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  • DOI: https://doi.org/10.1007/978-3-319-98923-5_4

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