# Autoregressive with Slack Time Series Model for Forecasting a Partially-Observed Dynamical Time Series

arXiv: https://arxiv.org/abs/2306.16593 · HTML: https://mlsanity.com/paper/2306.16593/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 28 Jun 2023.

## Builds on (most cited first, 6 of 6)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations](https://mlsanity.com/paper/2108.03561/) (2021)
- [Learning Latent Dynamics for Partially-Observed Chaotic Systems](https://mlsanity.com/paper/1907.02452/) (2019)
- [Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning](https://mlsanity.com/paper/2202.05750/) (2022)

## Abstract (arXiv)

This study delves into the domain of dynamical systems, specifically the forecasting of dynamical time series defined through an evolution function. Traditional approaches in this area predict the future behavior of dynamical systems by inferring the evolution function. However, these methods may confront obstacles due to the presence of missing variables, which are usually attributed to challenges in measurement and a partial understanding of the system of interest. To overcome this obstacle, we introduce the autoregressive with slack time series (ARS) model, that simultaneously estimates the evolution function and imputes missing variables as a slack time series. Assuming time-invariance and linearity in the (underlying) entire dynamical time series, our experiments demonstrate the ARS model's capability to forecast future time series. From a theoretical perspective, we prove that a 2-dimensional time-invariant and linear system can be reconstructed by utilizing observations from a single, partially observed dimension of the system.