# Inference of hidden common driver dynamics by anisotropic self-organizing neural networks

arXiv: https://arxiv.org/abs/2504.01811 · HTML: https://mlsanity.com/paper/2504.01811/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 2 Apr 2025.

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

- [Complete Inference of Causal Relations between Dynamical Systems](https://mlsanity.com/paper/1808.10806/) (2018)
- [Unsupervised Discovery of Temporal Structure in Noisy Data with Dynamical Components Analysis](https://mlsanity.com/paper/1905.09944/) (2019)
- [Recurrences reveal shared causal drivers of complex time series](https://mlsanity.com/paper/2301.13516/) (2023)
- [Manifold-adaptive dimension estimation revisited](https://mlsanity.com/paper/2008.03221/) (2020)
- [Reconstructing shared dynamics with a deep neural network](https://mlsanity.com/paper/2105.02322/) (2021)
- [Detecting Causality in the Frequency Domain with Cross-Mapping Coherence](https://mlsanity.com/paper/2407.20694/) (2024)

## Abstract (arXiv)

We are introducing a novel approach to infer the underlying dynamics of hidden common drivers, based on analyzing time series data from two driven dynamical systems. The inference relies on time-delay embedding, estimation of the intrinsic dimension of the observed systems, and their mutual dimension. A key component of our approach is a new anisotropic training technique applied to Kohonen's self-organizing map, which effectively learns the attractor of the driven system and separates it into submanifolds corresponding to the self-dynamics and shared dynamics. To demonstrate the effectiveness of our method, we conducted simulated experiments using different chaotic maps in a setup, where two chaotic maps were driven by a third map with nonlinear coupling. The inferred time series exhibited high correlation with the time series of the actual hidden common driver, in contrast to the observed systems. The quality of our reconstruction were compared and shown to be superior to several other methods that are intended to find the common features behind the observed time series, including linear methods like PCA and ICA as well as nonlinear methods like dynamical component analysis, canonical correlation analysis and even deep canonical correlation analysis.