# Using local dynamics to explain analog forecasting of chaotic systems

arXiv: https://arxiv.org/abs/2007.14216 · HTML: https://mlsanity.com/paper/2007.14216/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2020.

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

- [Evaluation of Machine Learning Techniques for Forecast Uncertainty Quantification](https://mlsanity.com/paper/2111.14844/) (2021)
- [Probability distributions for analog-to-target distances](https://mlsanity.com/paper/2101.10640/) (2021)
- [Missing the Butterfly and Predicting the Past: Features or Bugs of Accurate AI Weather Models?](https://mlsanity.com/paper/2608.25835/) (2026)
- [Noise-Induced Predictability Redistribution Across Forecast Horizons of Extreme Events in Chaotic Dynamics](https://mlsanity.com/paper/2609.27877/) (2026)

## Abstract (arXiv)

Analogs are nearest neighbors of the state of a system. By using analogs and their successors in time, one is able to produce empirical forecasts. Several analog forecasting methods have been used in atmospheric applications and tested on well-known dynamical systems. Although efficient in practice, theoretical connections between analog methods and dynamical systems have been overlooked. Analog forecasting can be related to the real dynamical equations of the system of interest. This study investigates the properties of different analog forecasting strategies by taking local approximations of the system's dynamics. We find that analog forecasting performances are highly linked to the local Jacobian matrix of the flow map, and that analog forecasting combined with linear regression allows to capture projections of this Jacobian matrix. The proposed methodology allows to estimate analog forecasting errors, and to compare different analog methods. These results are derived analytically and tested numerically on two simple chaotic dynamical systems.