New Method Improves Symbolic Regression for Complex Equations

Symbolic Regression (SR) aims to uncover underlying mathematical patterns from data. Existing machine learning methods for SR often fall short in truly understanding the mathematical and physical principles governing these expressions. While methods like AI Feynman made strides by leveraging mathematical properties, their simplification mechanisms are limited and struggle with complex equations, often relying on inefficient brute-force searches for sub-expressions. This new research proposes Deep Divide and Reduce in Symbolic Regression (DDRSR), a method grounded in rigorous mathematical deduction. DDRSR significantly expands the applicability of expression decomposition and reduction, eliminating the need for brute-force searches. It ensures both greater versatility and strict theoretical correctness in its approach. Empirical evaluations demonstrate that DDRSR's theoretical principles translate into substantial advantages in both decomposing complex expressions and achieving accurate numerical regression. The paper also discusses the practical scenarios where DDRSR is most applicable, its inherent limitations, and promising avenues for future research in this domain.