  Solutions of certain partial differential equations (PDEs) are often
represented by the steepest descent curves of corresponding functionals.
Minimizing movement scheme was developed in order to study such curves in
metric spaces. Especially, Jordan-Kinderlehrer-Otto studied the Fokker-Planck
equation in this way with respect to the Wasserstein metric space. In this
paper, we propose a deep learning-based minimizing movement scheme for
approximating the solutions of PDEs. The proposed method is highly scalable for
high-dimensional problems as it is free of mesh generation. We demonstrate
through various kinds of numerical examples that the proposed method accurately
approximates the solutions of PDEs by finding the steepest descent direction of
a functional even in high dimensions.
