Sparsifying priors for Bayesian uncertainty quantification in model discovery.

Area of Science:

• Dynamical Systems and Control Theory
• Machine Learning and Artificial Intelligence
• Scientific Computing

Background:

• Discovering governing equations from observational data is crucial for scientific understanding and prediction.
• Existing methods like Sparse Identification of Nonlinear Dynamics (SINDy) offer interpretability but can be sensitive to noise and data limitations.
• Quantifying uncertainty in discovered models is essential for reliable real-world applications.

Purpose of the Study:

• To develop a probabilistic model discovery method for identifying ordinary differential equations from multivariate data.
• To introduce Uncertainty Quantification SINDy (UQ-SINDy) that quantifies coefficient and model uncertainty.
• To enhance robustness, interpretability, and generalization capabilities of discovered dynamical models.

Main Methods:

• Leveraging the Sparse Identification of Nonlinear Dynamics (SINDy) framework.
• Employing sparse Bayesian inference for estimating SINDy coefficients, incorporating uncertainty quantification.
• Utilizing Markov chain Monte Carlo with spike and slab and regularized horseshoe priors for sparse inference.

Main Results:

• UQ-SINDy effectively quantifies uncertainty in SINDy coefficients and candidate function inclusion probabilities.
• The method demonstrates robustness against observation noise and requires significantly less data compared to existing techniques.
• Accurate dynamical models were discovered even with orders-of-magnitude less data and in the presence of noise.

Conclusions:

• UQ-SINDy provides a transformative approach to model discovery, offering enhanced interpretability and generalization.
• The probabilistic framework makes it suitable for real-world applications with limited and noisy observational data.
• This method advances the field of automated scientific discovery by incorporating rigorous uncertainty quantification.