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arXiv · 2501.02721

Learning Stochastic Nonlinear Dynamics with Embedded Latent Transfer Operators

Naichang Ke·Ryogo Tanaka·Yoshinobu Kawahara
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Abstract

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.

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Naichang Ke, Ryogo Tanaka, Yoshinobu Kawahara. 2025-01-06. Learning Stochastic Nonlinear Dynamics with Embedded Latent Transfer Operators. https://arxiv.org/abs/2501.02721

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