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Population-dynamics method with a multicanonical feedback control.

Takahiro Nemoto1,2, Freddy Bouchet2, Robert L Jack3

  • 1Laboratoire de Probabilités et Modèles Aléatoires, Sorbonne Paris Cité, UMR 7599 CNRS, Université Paris Diderot, 75013 Paris, France.

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|July 15, 2016
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Summary
This summary is machine-generated.

The Giardinà-Kurchan-Peliti method for Markov processes has errors, especially in complex systems. Introducing control forces, inspired by multicanonical methods, significantly improves accuracy for evaluating time-averaged quantities.

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Area of Science:

  • Statistical Physics
  • Computational Physics
  • Dynamical Systems

Background:

  • The Giardinà-Kurchan-Peliti (GKP) method is used for large deviations in Markov processes.
  • This method can suffer from systematic errors, particularly in systems with weak noise or many degrees of freedom.

Purpose of the Study:

  • To identify and mitigate systematic errors in the GKP population dynamics method.
  • To improve the accuracy of evaluating time-averaged quantities in Markov processes.

Main Methods:

  • Introduction of control forces into the GKP algorithm.
  • An iteration-and-feedback scheme, inspired by multicanonical sampling, to determine control forces.
  • Testing the improved method on a simple model system.

Main Results:

  • Demonstrated substantial mitigation of systematic errors in the GKP method.
  • Achieved significantly improved accuracy in evaluating large deviations of time-averaged quantities.
  • Validated the effectiveness of control forces in enhancing the population dynamics method.

Conclusions:

  • The proposed modification effectively addresses limitations of the original GKP method.
  • The approach shows promise for analyzing complex systems, including those near dynamical phase transitions.
  • Control forces offer a viable strategy for improving large deviation calculations in stochastic processes.