Sparse identification of nonlinear dynamics for rapid model recovery

Area of Science:

• Dynamical Systems Theory
• Machine Learning
• Nonlinear Dynamics

Background:

• Automated discovery of dynamical systems often relies on big data, which is not always available.
• Engineering systems can experience abrupt changes requiring rapid characterization from limited, noisy data.
• Existing machine learning techniques struggle with leveraging prior knowledge for model re-identification after system changes.

Purpose of the Study:

• To develop a framework for recovering parsimonious models of systems undergoing abrupt changes, particularly in low-data regimes.
• To enable rapid and efficient model updates by leveraging prior knowledge and minimizing changes to existing models.

Main Methods:

• Abrupt change detection by comparing estimated Lyapunov time with model predictions.
• Application of sparse identification of nonlinear dynamics (SINDy) regression to update existing models.
• Updating models through minimal additions, deletions, or modifications of existing terms.

Main Results:

• Demonstrated sparse model recovery for abrupt system changes in periodic and chaotic dynamical systems.
• Sparse updates to previously identified models showed improved performance with less data.
• The proposed method exhibited lower runtime complexity and reduced sensitivity to noise compared to identifying new models.

Conclusions:

• The abrupt-SINDy architecture offers a novel paradigm for efficient system model recovery post-abrupt change.
• This approach effectively handles low-data scenarios and leverages prior model information for faster adaptation.
• The method provides a robust solution for real-time system monitoring and control in dynamic environments.