הכרה מינימלית של מרחק למערכות דינמיות לא-רגליות

תקציר מקורי באנגליתarXiv:2601.04058v3 Announce Type: replace Abstract: We address the problem of classifying trajectories or sequences generated by nonlinear dynamical systems, where each class corresponds to a distinct dynamical system. We propose Dynafit, a kernel-based method that learns a distance metric between training data and the underlying dynamics. New observations are assigned to the class whose dynamics best fit the observations according to the learned metric.The learning algorithm approximates the Koopman operator, which globally linearizes the dynamics in a (potentially infinite-dimensional) feature space associated with a kernel function. The distance metric is computed in the feature space independently of its dimensionality by exploiting the kernel trick commonly used in machine learning. T