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

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.