  Solving high-dimensional optimal control problems in real-time is an
important but challenging problem, with applications to multi-agent path
planning problems, which have drawn increased attention given the growing
popularity of drones in recent years. In this paper, we propose a novel neural
network method called SympOCnet that applies the Symplectic network to solve
high-dimensional optimal control problems with state constraints. We present
several numerical results on path planning problems in two-dimensional and
three-dimensional spaces. Specifically, we demonstrate that our SympOCnet can
solve a problem with more than 500 dimensions in 1.5 hours on a single GPU,
which shows the effectiveness and efficiency of SympOCnet. The proposed method
is scalable and has the potential to solve truly high-dimensional path planning
problems in real-time.
