Inference of hidden common driver dynamics by anisotropic self-organizing neural networks
This addresses the challenge of uncovering shared underlying dynamics in complex systems, which is incremental as it builds on existing neural network and time series analysis techniques.
The paper tackles the problem of inferring hidden common driver dynamics from time series data of two driven systems, using an anisotropic self-organizing neural network approach, and demonstrates high correlation with the actual driver, outperforming methods like PCA, ICA, and deep canonical correlation analysis in simulated experiments.
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.