Enhancing Predictive Capabilities in Data-Driven Dynamical Modeling with Automatic Differentiation: Koopman and Neural ODE Approaches

arXiv:2310.06790v2 Announce Type: replace
Abstract: Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary learning (EDMD-DL) has garnered significant attention. Here we present a modification of EDMD-DL that concurrently determines both the dictionary of observables and the corresponding approximation of the Koopman operator. This innovation leverages automatic differentiation to facilitate gradient descent computations through the pseudoinverse. We …

abstract arxiv attention capabilities cs.lg data data-driven dictionary differentiation dynamic dynamics evolution modeling predictive systems type