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arXiv · 2412.08114

Modeling Latent Non-Linear Dynamical System over Time Series

Ren Fujiwara·Yasuko Matsubara·Yasushi Sakurai
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Abstract

We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms that incorporate long-term temporal dependencies are largely absent from existing studies. In this paper, we introduce a latent state to allow time-dependent modeling and formulate this problem as a dynamics estimation problem in latent states. We face multiple technical challenges, including (1) modeling latent non-linear dynamics and (2) solving circular dependencies caused by the presence of latent states. To tackle these challenging problems, we propose a new method, Latent Non-Linear equation modeling (LaNoLem), that can model a latent non-linear dynamical system and a novel alternating minimization algorithm for effectively estimating latent states and model parameters. In addition, we introduce criteria to control model complexity without human intervention. Compared with the state-of-the-art model, LaNoLem achieves competitive performance for estimating dynamics while outperforming other methods in prediction.

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Ren Fujiwara, Yasuko Matsubara, Yasushi Sakurai. 2024-12-11. Modeling Latent Non-Linear Dynamical System over Time Series. https://doi.org/10.1609/aaai.v39i11.33269

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