# Modeling Latent Non-Linear Dynamical System over Time Series

arXiv: https://arxiv.org/abs/2412.08114 · HTML: https://mlsanity.com/paper/2412.08114/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 32 references that are in the map.
- First posted on arXiv 11 Dec 2024.

## Builds on (most cited first, 9 of 9)

- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [A unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [Learning nonlinear dynamical systems from a single trajectory](https://mlsanity.com/paper/2004.14681/) (2020)
- [Learning concise representations for regression by evolving networks of trees](https://mlsanity.com/paper/1807.00981/) (2018)
- [Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systems](https://mlsanity.com/paper/2105.11558/) (2021)

## Built on by (most cited first, 4 of 4)

- [Fast Mining and Dynamic Time-to-Event Prediction over Multi-sensor Data Streams](https://mlsanity.com/paper/2601.04741/) (2026)
- [When to Retrain after Drift: A Data-Only Test of Post-Drift Data Size Sufficiency](https://mlsanity.com/paper/2603.09024/) (2026)
- [Modeling Dynamic Mixtures of Time-Delay Systems from Streaming Time Series](https://mlsanity.com/paper/2605.26191/) (2026)
- [AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regression](https://mlsanity.com/paper/2606.04930/) (2026)

## Abstract (arXiv)

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.