DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systems

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of these systems exhibit ergodicity and an attractor: a compact and highly complex manifold, to which trajectories converge in finite-time, that supports an invariant measure, i.e., a probability distribution that is invariant under the action of the dynamics, which dictates the long-term statistical behavior of the system. In this …

amplify converge cs.lg dynamics errors manifold math.ds positive systems