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Network inference in the nonequilibrium steady state.

Simon L Dettmer1, H Chau Nguyen2, Johannes Berg1

  • 1Institute for Theoretical Physics, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany.

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Summary
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Researchers developed methods to infer model parameters in nonequilibrium systems, which lack a steady-state characterization. This is crucial for applications like neural networks and gene regulatory networks.

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Area of Science:

  • Statistical physics
  • Complex systems modeling

Background:

  • Nonequilibrium systems lack a Boltzmann-like steady-state distribution.
  • This poses challenges for parameter inference in models without detailed balance.
  • Such systems are relevant to neural networks and gene regulatory networks.

Purpose of the Study:

  • To develop methods for inferring model parameters from nonequilibrium steady-state samples.
  • To address the challenge of parameter estimation in systems lacking detailed balance.

Main Methods:

  • Focus on the asymmetric Ising model as a paradigmatic example.
  • Developed an exact inference algorithm.
  • Created an approximate algorithm for weak interactions using mean-field expansion.

Main Results:

  • Demonstrated parameter inference from independent samples of the nonequilibrium steady state.
  • Derived expressions for magnetizations and spin correlations.
  • Established sufficiency of these observables for parameter inference.

Conclusions:

  • Parameter inference is achievable for nonequilibrium systems using steady-state samples.
  • The developed algorithms offer exact and approximate solutions.
  • Symmetries in mean-field expansion help distinguish dynamics.