  The quasipotential is a natural generalization of the concept of energy
functions to non-equilibrium systems. In the analysis of rare events in
stochastic dynamics, it plays a central role in characterizing the statistics
of transition events and the likely transition paths. However, computing the
quasipotential is challenging, especially in high dimensional dynamical systems
where a global landscape is sought. Traditional methods based on the dynamic
programming principle or path space minimization tend to suffer from the curse
of dimensionality. In this paper, we propose a simple and efficient machine
learning method to resolve this problem. The key idea is to learn an orthogonal
decomposition of the vector field that drives the dynamics, from which one can
identify the quasipotential. We demonstrate on various example systems that our
method can effectively compute quasipotential landscapes without requiring
spatial discretization or solving path-space optimization problems. Moreover,
the method is purely data driven in the sense that only observed trajectories
of the dynamics are required for the computation of the quasipotential. These
properties make it a promising method to enable the general application of
quasipotential analysis to dynamical systems away from equilibrium.
