Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control.

Area of Science:

• Dynamical Systems Science
• Computational Physics
• Data-Driven Modeling

Background:

• Sparse model identification (SINDy) discovers nonlinear dynamics from data but struggles with noise and limited datasets.
• Robustness is crucial for real-world applications where data is often imperfect.

Purpose of the Study:

• To develop a robust version of the SINDy algorithm using ensemble methods.
• To improve the accuracy and reliability of discovering nonlinear dynamical systems from noisy and limited data.
• To enable uncertainty quantification and probabilistic forecasting for identified models.

Main Methods:

• Bootstrap aggregating (bagging) was used to create an ensemble of SINDy models from data subsets.
• Aggregate model statistics were employed to determine candidate function inclusion probabilities.
• The ensemble-SINDy (E-SINDy) algorithm was applied to synthetic and real-world datasets.

Main Results:

• E-SINDy demonstrated significant improvements in accuracy and robustness compared to standard SINDy, especially with noisy and limited data.
• The algorithm successfully identified partial differential equations from data with twice the noise level of previous methods.
• E-SINDy accurately learned Lotka-Volterra dynamics from limited historical ecological data.

Conclusions:

• Ensemble-SINDy (E-SINDy) provides a robust and accurate method for discovering nonlinear dynamical systems from challenging datasets.
• The approach offers uncertainty quantification and has potential applications in active learning and model predictive control.
• E-SINDy is computationally efficient, making it a practical tool for complex system analysis.