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Modeling Unknown Stochastic Dynamical System Subject to External Excitation

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arxiv 2406.15747 v2 pith:WUZW6TOU submitted 2024-06-22 cs.LG cs.SYeess.SYmath.DS

Yuan Chen , Dongbin Xiu This is my paper
classification cs.LGcs.SYeess.SYmath.DS
keywords systemstochasticmethoddataexcitationunknownlearningsignals
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Network

    math.DS 2025-07 conditional novelty 6.0 of 10

    SGFNN learns a stochastic generating function via an autoencoder from paired state observations, yielding symplectic and more accurate long-term predictions for stochastic Hamiltonian systems than sFML.

  2. Generative AI Models for Learning Flow Maps of Stochastic Dynamical Systems in Bounded Domains

    stat.ML 2025-07 conditional novelty 5.0 of 10

    A hybrid generative model combining an exit probability neural network with a training-free diffusion model learns stochastic flow maps for SDEs in bounded domains with absorbing boundaries.

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