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Inference of time-ordered multibody interactions

Unai Alvarez-Rodriguez1,2, Luka V Petrović2, Ingo Scholtes2,3

  • 1University of Deusto, 48007 Bilbao, Spain.

Physical Review. E
|October 18, 2023
PubMed

Insights

We developed time-ordered multibody interactions to analyze complex systems with temporal and many-body dependencies. Our method efficiently extracts these interactions from data, robustly handling statistical errors.

Area of Science:

  • Complex Systems Science
  • Statistical Physics
  • Network Science

Background:

  • Complex systems often exhibit both temporal dynamics and intricate many-body interactions.
  • Understanding these coupled dependencies is crucial for modeling and prediction.
  • Existing methods may struggle to capture the full complexity of such systems.

Purpose of the Study:

  • To introduce a novel framework for describing complex systems using time-ordered multibody interactions.
  • To develop an algorithm for extracting these interactions from observational data.
  • To provide a measure for characterizing the complexity of interaction ensembles.

Main Methods:

  • Decomposition of multivariate Markov chain dynamics into time-ordered multibody interactions.
  • Development of a data-driven algorithm for interaction extraction.
  • Introduction of a complexity measure for interaction ensembles.
  • Experimental validation of algorithm robustness and efficiency.

Main Results:

  • Demonstrated decomposition of Markov chain dynamics into time-ordered multibody interactions.
  • Presented a robust and efficient algorithm for extracting these interactions from system dynamics.
  • Showcased the ability to infer parsimonious interaction ensembles.

Conclusions:

  • Time-ordered multibody interactions provide a powerful framework for complex systems.
  • The developed algorithm offers a reliable method for analyzing temporal and many-body dependencies.
  • This approach enhances our ability to model and understand complex system behaviors.

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