TAD-Div: A data-driven framework for quantifying the similarity of nonlinear dynamical systems

Area of Science:

• Nonlinear Dynamics
• Complex Systems Analysis
• Machine Learning for Science

Background:

• Quantifying similarity between nonlinear dynamical systems from data is challenging.
• Existing methods struggle with noise, high dimensionality, and modeling system evolution.
• A robust, data-driven approach is needed for accurate system comparison.

Purpose of the Study:

• Introduce TAD-Div (TCN-Attention-based Dynamics Divergence), a novel framework for comparing nonlinear dynamical systems.
• Address limitations of existing methods in robustness and modeling evolutionary rules.
• Provide a tool for sensitive analysis of system dynamics and anomaly detection.

Main Methods:

• Propose TAD-Div framework based on cross-reconstructability.
• Introduce Dynamic Attention (DynAttn) mechanism integrating Temporal Convolutional Networks (TCNs).
• Quantify dynamical divergence using cross- and self-reconstruction errors.

Main Results:

• TAD-Div demonstrates superior performance and robustness across diverse nonlinear systems and a bearing fault dataset.
• Outperforms baselines in high-dimensional and noisy conditions.
• Exhibits sensitivity to parameter variations and strong noise resilience.

Conclusions:

• TAD-Div offers a rigorous, data-driven tool for comparing complex dynamical systems.
• The framework is effective for characterizing underlying dynamical rules.
• Demonstrates practical applicability in anomaly detection tasks.