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Tensor Network Renormalization as an Ultra-calculus for Complex System Dynamics

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Sustainable Interdependent Networks II

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

Abstract

In this chapter, following the previous one, we briefly present the modern approach to real-space renormalization group (RG) theory based on tensor network formulations which was developed during the last two decades. The aim of this sequel is to suggest a novel framework based on tensor networks in order to find the fixed points of complex systems via coarse-graining. The main result of RG is that it provides a systematic way to study the collective dynamics of a large ensemble of elements that interact according to a complex underlying network topology. RG explicitly seeks the fixed points of the complex system in the space of interactions and unravels the universality class of the complex system as well as calculates a plethora of important observables. 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.

“The belief on the part of many that the renormalisability of the universe is a constraint on an underlying Theory of Everything rather than an emergent property is nothing but an unfalsifiable article of faith.”

Laughlin and Pines [32]

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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). Tensor Network Renormalization as an Ultra-calculus for Complex System Dynamics. 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_5

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  • DOI: https://doi.org/10.1007/978-3-319-98923-5_5

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