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

Area of Science:

• Complex Systems Science
• Machine Learning
• Dynamical Systems Theory

Background:

• Inferring hidden causal structures in nonlinear dynamical systems from observed time series is a significant challenge.
• Existing methods often struggle with the complexity and nonlinearities inherent in such systems.

Purpose of the Study:

• To introduce a novel neural network-based approach, the Anisotropic Self-Organizing Map (ASOM), for unsupervised learning of hidden common drivers in nonlinear dynamical systems.
• To enable the precise decomposition of attractor manifolds into autonomous and shared components of the dynamics.

Main Methods:

• Integration of time-delay embedding, intrinsic dimension estimation, and an anisotropic training scheme for Kohonen's self-organizing map.
• Validation through simulations of chaotic maps with hidden nonlinear drivers.
• Comparison against established methods like PCA, ICA, and deep canonical correlation analysis.

Main Results:

• The ASOM successfully inferred time series strongly correlated with the actual hidden common driver in simulations.
• ASOM demonstrated superior accuracy and robustness in recovering latent dynamics compared to benchmark methods.
• The method effectively decomposes attractor manifolds into distinct dynamic components.

Conclusions:

• ASOM provides a powerful and accurate tool for unsupervised learning and uncovering hidden causal structures in complex systems.
• The anisotropic training scheme is key to ASOM's effectiveness in separating shared and autonomous dynamics.
• This approach advances the analysis of nonlinear time series data and the understanding of complex system interactions.