Learning Stochastic Nonlinear Dynamics with Embedded Latent Transfer Operators

Naichang Ke, Ryogo Tanaka, Yoshinobu Kawahara
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:4861-4869, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-ke25a, title = {Learning Stochastic Nonlinear Dynamics with Embedded Latent Transfer Operators}, author = {Ke, Naichang and Tanaka, Ryogo and Kawahara, Yoshinobu}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {4861--4869}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/ke25a/ke25a.pdf}, url = {https://proceedings.mlr.press/v258/ke25a.html}, 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.} }
Endnote
%0 Conference Paper %T Learning Stochastic Nonlinear Dynamics with Embedded Latent Transfer Operators %A Naichang Ke %A Ryogo Tanaka %A Yoshinobu Kawahara %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-ke25a %I PMLR %P 4861--4869 %U https://proceedings.mlr.press/v258/ke25a.html %V 258 %X 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.
APA
Ke, N., Tanaka, R. & Kawahara, Y.. (2025). Learning Stochastic Nonlinear Dynamics with Embedded Latent Transfer Operators. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:4861-4869 Available from https://proceedings.mlr.press/v258/ke25a.html.

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