Learning stochastic dynamics with statistics-informed neural network
Abstract
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 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.
- Publication:
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Journal of Computational Physics
- Pub Date:
- February 2023
- DOI:
- 10.1016/j.jcp.2022.111819
- arXiv:
- arXiv:2202.12278
- Bibcode:
- 2023JCoPh.47411819Z
- Keywords:
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- Scientific machine learning;
- Recurrent neural network;
- Reduced-order stochastic modeling;
- Rare events;
- Computer Science - Machine Learning;
- Condensed Matter - Statistical Mechanics;
- Computer Science - Artificial Intelligence;
- Mathematics - Dynamical Systems;
- Physics - Computational Physics
- E-Print:
- doi:10.1016/j.jcp.2022.111819