Modeling Latent Non-Linear Dynamical System over Time Series

TL;DR

This paper introduces LaNoLem, a novel method for modeling latent non-linear dynamical systems from time series data, effectively estimating dynamics and predicting future states with minimal human intervention.

Contribution

The paper proposes LaNoLem, a new approach that models latent non-linear dynamics and includes an alternating minimization algorithm for parameter and state estimation.

Findings

LaNoLem achieves competitive dynamics estimation performance.

LaNoLem outperforms existing methods in prediction accuracy.

The method effectively manages model complexity without human input.

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.