  We present a novel yet simple deep learning approach, called input gradient
annealing neural network (IGANN), for solving stationary Fokker-Planck
equations. Traditional methods, such as finite difference and finite elements,
suffer from the curse of dimensionality. Neural network based algorithms are
meshless methods, which can avoid the curse of dimensionality. However, at low
temperature, when directly solving a stationary Fokker-Planck equation with
more than two metastable states in the generalized potential landscape, the
small eigenvalue introduces numerical difficulties due to a large condition
number. To overcome these problems, we introduce the IGANN method, which uses a
penalty of negative input gradient annealing during the training. We
demonstrate that the IGANN method can effectively solve high-dimensional and
low-temperature Fokker-Planck equations through our numerical experiments.
