An information-based model selection criterion for data-driven model discovery.

Area of Science:

• Computational Physics
• Applied Mathematics
• Data Science

Background:

• Data-driven model discovery (DDMD) algorithms extract symbolic models from data.
• Current DDMD methods struggle with balancing model fit and sparsity, often requiring manual tuning and risking overfitting.
• Model selection can be sensitive to initialization and training procedures.

Purpose of the Study:

• To develop an automated and adaptive sparse regression algorithm for DDMD.
• To introduce a novel information criterion, sample-length-scaling logarithmic information criterion (SLIC), for robust model selection.
• To demonstrate SLIC's superiority over existing criteria in identifying accurate and sparse models.

Main Methods:

• Developed a sparse regression algorithm that automatically generates candidate models.
• Implemented a novel sample-length-scaling logarithmic information criterion (SLIC) for model evaluation.
• Validated the algorithm on synthetic data from nonlinear ordinary and partial differential equations.

Main Results:

• SLIC significantly outperforms popular information criteria in extracting correct models from differential equation data.
• The algorithm successfully discovered interpretable models from experimental fluid dynamics and nanotechnology datasets.
• The discovered models yielded new, testable predictions.

Conclusions:

• The proposed SLIC-based sparse regression algorithm automates and improves DDMD.
• SLIC offers a robust method for balancing model goodness-of-fit and sparsity.
• This approach facilitates the discovery of predictive, interpretable models from complex data.