A deep learning method for solving Fokker-Planck equations

Understand

The time evolution of the probability distribution of a stochastic differential equation follows the Fokker-Planck equation, which usually has an unbounded, high-dimensional domain.

• Inspired by our early study in \cite{li2018data}, we propose a mesh-free Fokker-Planck solver, in which the solution to the Fokker-Planck equation is now represented by a neural network.
• The presence of the differential operator in the loss function improves the accuracy of the neural network representation and reduces the the demand of data in the training process.
• Several high dimensional numerical examples are demonstrated.