mlsanityData to 7 Oct 2026

Modeling Unknown Stochastic Dynamical System Subject to External Excitation

arXiv 2406.15747 ↗First posted 22 Jun 2024cs.LG cs.SY eess.SYcited by 7

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Abstract (arXiv)

We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the stochastic system are unavailable. However, short bursts of input/output (I/O) data consisting of certain known excitation signals and their corresponding system responses are available. When a sufficient amount of such I/O data are available, our method is capable of learning the unknown dynamics and producing an accurate predictive model for the stochastic responses of the system subject to arbitrary excitation signals not in the training data. Our method has two key components: (1) a local approximation of the training I/O data to transfer the learning into a parameterized form; and (2) a generative model to approximate the underlying unknown stochastic flow map in distribution. After presenting the method in detail, we present a comprehensive set of numerical examples to demonstrate the performance of the proposed method, especially for long-term system predictions.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 33 of its 59 references that are in the map. First posted on arXiv 22 Jun 2024.

Builds on

33 of 59 references.

References · 33

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2016Density estimation using Real NVPcited by 2,029
  4. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  5. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  6. 2018Neural Importance Samplingcited by 154
  7. 2017Sparse identification of nonlinear dynamics for model predictive control in the low-data limitcited by 139
  8. 2016Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive controlcited by 134
  9. 2014Dynamic mode decomposition with controlcited by 128
  10. 2018Data Driven Governing Equations Approximation Using Deep Neural Networkscited by 94
  11. 2018Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systemscited by 88
  12. 2018Latent Space Policies for Hierarchical Reinforcement Learningcited by 66
21 more
  1. 2020Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networkscited by 52
  2. 2017Extracting Sparse High-Dimensional Dynamics from Limited Datacited by 50
  3. 2016Generalizing Koopman Theory to allow for inputs and controlcited by 49
  4. 2020Modeling Continuous Stochastic Processes with Dynamic Normalizing Flowscited by 37
  5. 2021Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learningcited by 37
  6. 2017A-NICE-MC: Adversarial Training for MCMCcited by 36
  7. 2021Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow modelscited by 34
  8. 2021Computational Graph Completioncited by 28
  9. 2016Iterative Gaussianization: from ICA to Random Rotationscited by 26
  10. 2023Learning Stochastic Dynamical System via Flow Map Operatorcited by 24
  11. 2018Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matchingcited by 23
  12. 2020Learning reduced systems via deep neural networks with memorycited by 20
  13. 2017Koopman-based lifting techniques for nonlinear systems identificationcited by 18
  14. 2021Learning the temporal evolution of multivariate densities via normalizing flowscited by 18
  15. 2023Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarkscited by 18
  16. 2022One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernelscited by 15
  17. 2022MultiAuto-DeepONet: A Multi-resolution Autoencoder DeepONet for Nonlinear Dimension Reduction, Uncertainty Quantification and Operator Learning of Forward and Inverse Stochastic Problemscited by 13
  18. 2023Modeling Unknown Stochastic Dynamical System via Autoencodercited by 12
  19. 2023Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systemscited by 11
  20. 2021Extracting stochastic dynamical systems with α-stable L'evy noise from datacited by 8
  21. 2024DynGMA: a robust approach for learning stochastic differential equations from datacited by 8

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 4; 2026: 2.

7 papers.

  1. 2024Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systemscited by 5
  2. 2025Generative AI Models for Learning Flow Maps of Stochastic Dynamical Systems in Bounded Domainscited by 3
  3. 2025Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Networkcited by 1
  4. 2025A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Seriescited by 1
  5. 2025Identifying Unknown Stochastic Dynamics via Finite expression methodscited by 0
  6. 2026Data-driven Effective Modeling of Stochastic Chemical Reaction Networkscited by 0
  7. 2026Very Exciting: Zero-Shot Model Predictive Control of Buildings via Excitation-Based Generalized Transfer Learning Modelscited by 0