Exploring multi-view symbolic regression methods in physical sciences

Area of Science:

• * Computational Physics
• * Scientific Machine Learning
• * Data Science

Background:

• * Mathematical functions are crucial for understanding natural phenomena.
• * Symbolic Regression (SR) automates the discovery of interpretable equations from data.
• * Multi-view Symbolic Regression (MvSR) extends SR to leverage multiple datasets, reducing overfitting and data scarcity.

Purpose of the Study:

• * To benchmark and compare the performance of different MvSR implementations.
• * To identify features that contribute to the generation of high-quality, parsimonious models.
• * To provide recommendations for future MvSR algorithm development.

Main Methods:

• * Evaluation of MvSR algorithms (Operon, PySR, ϕ-SO, eggp) on diverse real-world datasets.
• * Comparative analysis of model accuracy, interpretability, and parameter efficiency.
• * Identification of key algorithmic features influencing model performance.

Main Results:

• * All tested MvSR implementations frequently achieve good accuracy on real-world data.
• * Models generated often feature a small number of parameters, enhancing interpretability.
• * Certain algorithmic features were found to significantly improve the quality of discovered models.

Conclusions:

• * MvSR is a powerful technique for discovering scientific equations from multiple datasets.
• * Algorithmic design choices significantly impact the effectiveness of MvSR tools.
• * Guidelines are proposed to steer future advancements in MvSR for enhanced scientific discovery.