Trend to equilibrium for the kinetic Fokker-Planck equation via the neural network approach

•Deep Neural Network approach to solve the kinetic Fokker-Planck equation in a bounded interval.•Theoretical evidence on the relationship between the Deep Neural Network solutions and the a priori analytic solutions.•There exists a sequence of weights such that the total sum of loss functions converges to 0.•The neural networks equipped with such weights converge to an analytic solution.•The long-time asymptotics of the neural network solutions to the Fokker-Planck equation under various boundary conditions.