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Duality between predictability and reconstructability in complex systems

Author

Listed:
  • Charles Murphy

    (Université Laval
    Université Laval)

  • Vincent Thibeault

    (Université Laval
    Université Laval)

  • Antoine Allard

    (Université Laval
    Université Laval)

  • Patrick Desrosiers

    (Université Laval
    Université Laval
    Centre de recherche CERVO)

Abstract

Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here, we find an intricate relationship between predictability and reconstructability using an information-theoretical point of view. We use the mutual information between a random graph and a stochastic process evolving on this random graph to quantify their codependence. Then, we show how the uncertainty coefficients, which are intimately related to that mutual information, quantify our ability to reconstruct a graph from an observed time series, and our ability to predict the evolution of a process from the structure of its interactions. We provide analytical calculations of the uncertainty coefficients for many different systems, including continuous deterministic systems, and describe a numerical procedure when exact calculations are intractable. Interestingly, we find that predictability and reconstructability, even though closely connected by the mutual information, can behave differently, even in a dual manner. We prove how such duality universally emerges when changing the number of steps in the process. Finally, we provide evidence that predictability-reconstruction dualities may exist in dynamical processes on real networks close to criticality.

Suggested Citation

  • Charles Murphy & Vincent Thibeault & Antoine Allard & Patrick Desrosiers, 2024. "Duality between predictability and reconstructability in complex systems," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
  • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-48020-x
    DOI: 10.1038/s41467-024-48020-x
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    References listed on IDEAS

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