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A transfer learning method to solve Fokker-Planck equation based on the equivalent linearization.

Gege Wang1, Xiaolong Wang1,2, Qi Liu3

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This study introduces a novel transfer learning method to efficiently solve the Fokker-Planck (FP) equation for stochastic systems. The approach accelerates computation and maintains accuracy for complex systems.

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Area of Science:

  • Computational Physics
  • Applied Mathematics
  • Machine Learning

Background:

  • Solving the Fokker-Planck (FP) equation is essential for analyzing stochastic systems.
  • Current methods can be computationally intensive, limiting their application.
  • There is a need for more efficient and accurate solution techniques.

Purpose of the Study:

  • To develop an efficient transfer learning-based method for solving the Fokker-Planck equation.
  • To accelerate the training process for solving complex stochastic systems.
  • To demonstrate the method's accuracy and generalization capabilities.

Main Methods:

  • Equivalent linearization to unify stochastic differential equations.
  • A pre-trained neural network framework inspired by transfer learning.
  • Numerical experiments on one- and two-dimensional systems with Gaussian and Lévy noise.

Main Results:

  • The proposed transfer learning method significantly reduces training time for solving FP equations.
  • The method accurately learns the contours of FP equations.
  • Effective for systems with Gaussian and Lévy noise.

Conclusions:

  • The transfer learning approach offers a computationally efficient solution for the Fokker-Planck equation.
  • The method exhibits strong generalization capabilities across different stochastic systems.
  • This technique enhances the study of stochastic systems by improving computational efficiency.