A method that speeds the numerical discovery of fixed points (steady solutions) of the two-dimensional Kuramoto-Sivashinsky equation by training a deep reinforcement-learning agent to propose good initial guesses for the Jacobian-Free Newton-Krylov solver. The agent's reward favors candidate states whose spectral structure resembles that of known fixed points, and parallel reinforcement learning is used to steer trajectories between fixed points. The approach uncovers previously unreported fixed points and is offered as a template for other high-dimensional chaotic dynamical systems.
This study accelerates the search for fixed points (steady solutions) of the two-dimensional Kuramoto-Sivashinsky equation, a nonlinear partial differential equation that exhibits chaotic spatio-temp…