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Area of Science:

  • Statistical Physics
  • Nonequilibrium Systems
  • Stochastic Processes

Background:

  • Large deviation functions characterize fluctuations in physical systems, particularly nonequilibrium processes.
  • Stochastic algorithms, like the power method, are adapted for analyzing Markov processes and diffusions.
  • Previous work introduced an adaptive power method for risk-sensitive control and continuous-time diffusions.

Purpose of the Study:

  • To conduct an in-depth performance analysis of an adaptive power method for learning large deviation functions.
  • To investigate the algorithm's convergence near dynamical phase transitions.
  • To evaluate the impact of learning rate and transfer learning on convergence speed.

Main Methods:

  • Application of a stochastic algorithm based on the power method.
  • Adaptive learning of large deviation functions for Markov processes.
  • Analysis of convergence rates and the effect of transfer learning.
  • Testing the algorithm on a random walk's mean degree on an Erdős-Rényi random graph.

Main Results:

  • The adaptive power method demonstrates efficiency in analyzing dynamical phase transitions.
  • Convergence speed is studied as a function of the learning rate.
  • Transfer learning was incorporated and its effects analyzed.
  • The method proved effective for distinguishing between high-degree and low-degree trajectories in the test case.

Conclusions:

  • The adaptive power method is a performant and complex-efficient tool for computing large deviation functions.
  • The algorithm excels in analyzing systems near dynamical phase transitions.
  • It offers advantages over existing algorithms for studying fluctuations in Markov processes.