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Machine learning framework for computing the most probable paths of stochastic dynamical systems.

Yang Li1,2, Jinqiao Duan2, Xianbin Liu1

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Summary
This summary is machine-generated.

This study introduces a machine learning framework to accurately compute the most probable paths in nonlinear systems. This method enhances understanding of noise-induced transitions and rare events in complex systems.

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Area of Science:

  • Nonlinear dynamics
  • Stochastic processes
  • Computational physics

Background:

  • Noise-induced transitions are crucial in nonlinear systems.
  • Understanding these transitions requires computing most probable paths.
  • Current methods like the shooting method struggle with high-dimensional systems.

Purpose of the Study:

  • To develop a novel machine learning framework for computing most probable paths.
  • To overcome limitations of traditional methods in high-dimensional stochastic systems.
  • To accurately model transition phenomena in nonlinear systems.

Main Methods:

  • Reformulated the boundary value problem of a Hamiltonian system.
  • Designed a neural network to solve the Onsager-Machlup action functional.
  • Applied the framework to systems with Gaussian (Brownian) and non-Gaussian (Lévy) noise.

Main Results:

  • The machine learning framework accurately computes most probable paths.
  • Demonstrated efficacy and accuracy on several prototypical examples.
  • Successfully handled both Gaussian and non-Gaussian noise in stochastic systems.

Conclusions:

  • The developed machine learning approach is effective for analyzing rare events in stochastic systems.
  • This method provides a powerful tool for exploring internal mechanisms of noise-driven transitions.
  • Offers a viable alternative to traditional methods for high-dimensional problems.