mlsanityData to 14 Oct 2026

Learning Stochastic Dynamics with Statistics-Informed Neural Network

arXiv 2202.12278 ↗First posted 24 Feb 2022cs.LG cond-mat.stat-mech cs.AIcited by 16

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Abstract (arXiv)

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.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). Builds on 17 of its 56 references that are in the map. First posted on arXiv 24 Feb 2022.

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17 of 56 references.

References · 17

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5 more
  1. 2019Learning interaction kernels in heterogeneous systems of agents from multiple trajectoriescited by 25
  2. 2020Learning interaction kernels in stochastic systems of interacting particles from multiple trajectoriescited by 25
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Citing papers per year: 2023: 7; 2024: 1; 2025: 3; 2026: 5.

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