The prediction of stochastic dynamical systems and the capture of dynamical behaviors are
profound problems. In this article, we propose a data-driven framework combining Reservoir …

We extend the methodology in Yang et al.[SIAM J. Appl. Dyn. Syst. 22, 269–310 (2023)] to
learn autonomous continuous-time dynamical systems from invariant measures. The …

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian
systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic …

Invariant measures are widely used to compare chaotic dynamical systems, as they offer
robustness to noisy data, uncertain initial conditions, and irregular sampling. However, large …

Learning stochastic differential equations (SDEs) from observational data via neural
networks is an important means of quantifying uncertainty in dynamical systems. The …

Revealing hidden stochastic dynamics from observation data is of great importance in
applications. Traditional methods usually require a large number of independent trajectories …

Detecting and predicting the behavior of Hamiltonian systems via machine learning has
been drawing increasing attentions in recent years. In this paper, we propose a data-driven …

Recent advances in data science are opening up new research fields and broadening the
range of applications of stochastic dynamical systems. Considering the complexities in real …