Algorithm for solving the Fokker-Planck equation with a neural network method

Background: Thermal fission rates have been calculated with various methods, such as Bohr-Wheeler theory, Kramers's formula, stochastic dynamics, and the Fokker-Planck equation (FPE). How to reasonably calculate fission rates is still a challenging subject.Purpose: The FPE provides a powerful statistical model to describe nuclear fission. However, it is very difficult to solve with general numerical methods. We propose an algorithm with a neural network method to actually and accurately solve the FPE and, therefore, to calculate fission rates.Methods: The proposed algorithm is used to obtain the probability distributions of the FPE. Fission rates and half-lives are calculated with the resultant probability distributions.Results: Plausible predictions of fission half-lives match the experiment data well. The thermal fission rates and fission times are also consistent with various microscopic calculation results.Conclusions: The results show that the FPE can be solved reliably and feasibly with our proposed algorithm with a reasonable accuracy. This algorithm can be used to analyze various transport problems.