Learning Stochastic Nonlinear Dynamics with Embedded Latent Transfer Operators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909018506657792 |
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| author | Ke, Naichang Tanaka, Ryogo Kawahara, Yoshinobu |
| author_facet | Ke, Naichang Tanaka, Ryogo Kawahara, Yoshinobu |
| contents | We consider an operator-based latent Markov representation of a stochastic nonlinear dynamical system, where the stochastic evolution of the latent state embedded in a reproducing kernel Hilbert space is described with the corresponding transfer operator, and develop a spectral method to learn this representation based on the theory of stochastic realization. The embedding may be learned simultaneously using reproducing kernels, for example, constructed with feed-forward neural networks. We also address the generalization of sequential state-estimation (Kalman filtering) in stochastic nonlinear systems, and of operator-based eigen-mode decomposition of dynamics, for the representation. Several examples with synthetic and real-world data are shown to illustrate the empirical characteristics of our methods, and to investigate the performance of our model in sequential state-estimation and mode decomposition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_02721 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Stochastic Nonlinear Dynamics with Embedded Latent Transfer Operators Ke, Naichang Tanaka, Ryogo Kawahara, Yoshinobu Machine Learning I.2.6 We consider an operator-based latent Markov representation of a stochastic nonlinear dynamical system, where the stochastic evolution of the latent state embedded in a reproducing kernel Hilbert space is described with the corresponding transfer operator, and develop a spectral method to learn this representation based on the theory of stochastic realization. The embedding may be learned simultaneously using reproducing kernels, for example, constructed with feed-forward neural networks. We also address the generalization of sequential state-estimation (Kalman filtering) in stochastic nonlinear systems, and of operator-based eigen-mode decomposition of dynamics, for the representation. Several examples with synthetic and real-world data are shown to illustrate the empirical characteristics of our methods, and to investigate the performance of our model in sequential state-estimation and mode decomposition. |
| title | Learning Stochastic Nonlinear Dynamics with Embedded Latent Transfer Operators |
| topic | Machine Learning I.2.6 |
| url | https://arxiv.org/abs/2501.02721 |