Sparse Identification of Nonlinear Dynamics With Library Optimization Mechanism: Recursive Long-Term Prediction...

Area of Science:

• Dynamical Systems Theory
• Machine Learning
• Scientific Computing

Background:

• Sparse identification of nonlinear dynamics (SINDy) is a data-driven method for discovering governing equations.
• A key challenge in SINDy is the manual design of the candidate basis function library.
• Existing SINDy methods often ensure only one-step-ahead prediction accuracy, limiting long-term reliability.

Purpose of the Study:

• To propose a novel approach, SINDy with a library optimization mechanism (SINDy-LOM), to automate library design.
• To enhance the reliability of discovered dynamical models through recursive long-term (RLT) prediction accuracy.
• To reduce the user burden associated with traditional SINDy library construction.

Main Methods:

• SINDy-LOM combines sparse regression with a learning strategy for library optimization.
• A two-layer optimization architecture is employed: inner layer for model extraction, outer layer for basis function optimization.
• Basis functions are parametrized and optimized based on recursive long-term prediction accuracy.

Main Results:

• SINDy-LOM successfully optimizes the basis function library, reducing manual effort.
• The approach yields parsimonious, interpretable, and usable closed-form dynamical models.
• RLT perspective enhances model reliability compared to traditional SINDy's one-step-ahead prediction.

Conclusions:

• SINDy-LOM offers an effective solution for automated library design in SINDy.
• The method provides more reliable dynamical models suitable for long-term predictions.
• This approach significantly advances the usability and applicability of data-driven equation discovery.