mlsanityData to 14 Oct 2026

Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems

arXiv 2408.14821 ↗First posted 27 Aug 2024cs.LG cs.NA math.NAcited by 5

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Abstract (arXiv)

We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are available. By utilizing the observation data, our proposed method is capable of constructing a generative stochastic model that can accurately capture the effective dynamics of the slow variables in distribution. We present a comprehensive set of numerical examples to demonstrate the performance of the proposed method.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 24 of its 46 references that are in the map. First posted on arXiv 27 Aug 2024.

Builds on

24 of 46 references.

References · 24

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2016Density estimation using Real NVPcited by 2,042
  4. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  5. 2017Masked Autoregressive Flow for Density Estimationcited by 684
  6. 2018Data Driven Governing Equations Approximation Using Deep Neural Networkscited by 96
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  8. 2020Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networkscited by 52
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  11. 2021Computational Graph Completioncited by 28
  12. 2021Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Spacecited by 25
12 more
  1. 2023Learning Stochastic Dynamical System via Flow Map Operatorcited by 24
  2. 2018Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matchingcited by 23
  3. 2018Model Reduction with Memory and the Machine Learning of Dynamical Systemscited by 21
  4. 2020Learning reduced systems via deep neural networks with memorycited by 20
  5. 2023Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarkscited by 18
  6. 2022One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernelscited by 15
  7. 2022MultiAuto-DeepONet: A Multi-resolution Autoencoder DeepONet for Nonlinear Dimension Reduction, Uncertainty Quantification and Operator Learning of Forward and Inverse Stochastic Problemscited by 13
  8. 2023Modeling Unknown Stochastic Dynamical System via Autoencodercited by 12
  9. 2024Modeling Unknown Stochastic Dynamical System Subject to External Excitationcited by 7
  10. 2021Nonlinear model reduction for slow-fast stochastic systems near unknown invariant manifoldscited by 4
  11. 2022Learning effective dynamics from data-driven stochastic systemscited by 3
  12. 2021Discovery of slow variables in a class of multiscale stochastic systems via neural networkscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 2.

5 papers.

  1. 2025Generative AI Models for Learning Flow Maps of Stochastic Dynamical Systems in Bounded Domainscited by 3
  2. 2025Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Networkcited by 1
  3. 2025Self-induced stochastic resonance: A physics-informed machine learning approachcited by 0
  4. 2026Data-driven Effective Modeling of Stochastic Chemical Reaction Networkscited by 0
  5. 2026Memory-Conditioned Diffusion Model for Generalized Langevin Dynamicscited by 0