Learning stochastic dynamics with statistics-informed neural network

We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by universal approximation theorem systems, which we in this paper, and the projection-operator formalism modeling. devise mechanisms training model to reproduce correct statistical behavior of target process. Numerical simulation results demonstrate that well-trained SINN can reliably approximate both Markovian non-Markovian dynamics. applicability coarse-graining problems modeling transition Furthermore, show obtained reduced-order be trained on temporally coarse-grained data hence is well suited rare-event simulations.