Learning Stochastic Dynamics with Statistics-Informed Neural Network
This work addresses the challenge of modeling complex stochastic systems for researchers in computational science and machine learning, though it appears incremental as it builds on existing neural network and projection-operator approaches.
The authors tackled the problem of learning stochastic dynamics from data by introducing a statistics-informed neural network (SINN) framework, which reliably approximates both Markovian and non-Markovian processes and is applicable to coarse-graining and rare-event simulations.
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 a universal approximation theorem for stochastic systems, which we introduce in this paper, and the projection-operator formalism for stochastic modeling. We devise mechanisms for training the neural network model to reproduce the correct \emph{statistical} behavior of a target stochastic process. Numerical simulation results demonstrate that a well-trained SINN can reliably approximate both Markovian and non-Markovian stochastic dynamics. We demonstrate the applicability of SINN to coarse-graining problems and the modeling of transition dynamics. Furthermore, we show that the obtained reduced-order model can be trained on temporally coarse-grained data and hence is well suited for rare-event simulations.