Universal Construction of Generalized Lyapunov Functions for Nonlinear Dynamical Systems Using Physics-Informed Neural Networks (opens in new tab)

A scalar potential landscape is one of the most useful ways to understand the stability and transition of a dynamical system. For non-gradient dynamics, however, the construction of a global Lyapunov-type scalar for nonlinear flows with recurrent structures remains a major obstacle. We introduce the generalized Lyapunov function, a scalar function that is non-increasing along deterministic trajectories, as a unifying notion of nonequilibrium p...