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

We introduce the Anisotropic Self-Organizing Map (ASOM), a novel neural network-based approach for inferring hidden common drivers in nonlinear dynamical systems from observed time series. Grounded in topological theorems, our method integrates time-delay embedding, intrinsic dimension estimation, and a new anisotropic training scheme for Kohonen’s self-organizing map, enabling the precise decomposition of attractor manifolds into autonomous and shared components of the dynamics. We validated ASOM through simulations involving chaotic maps, where two driven systems were influenced by a hidden nonlinear driver. The inferred time series showed a strong correlation with the actual hidden common driver, unlike the observed systems. We further compared our reconstruction performance against several established methods for identifying shared features in time series, including PCA, kernel PCA, ICA, dynamical component analysis, canonical correlation analysis, deep canonical correlation analysis, traditional self-organizing map, and recent recurrence-based approaches. Our results demonstrate ASOM’s superior accuracy and robustness in recovering latent dynamics, providing a powerful tool for unsupervised learning of hidden causal structures in complex systems.