Decomposable Symbolic Regression Using Transformers and Neural Network-Assisted Genetic Algorithms

🎤 I will be presenting my dissertation work on Symbolic Regression at GREYC on April 3rd.

📚 One of the goals of science is to discover laws that serve as causal explanations for the observable world. Such discoveries may stem from distilling experimental data into analytical equations that allow interpretation of their underlying natural laws. This process is known as equation learning or symbolic regression (SR). Nevertheless, most SR methods prioritize minimizing prediction error over identifying the governing equations, often producing overly complex or inaccurate expressions. To address this, in this talk, I present a decomposable SR method that generates interpretable multivariate expressions leveraging transformer models, genetic algorithms (GAs), and genetic programming (GP). It first generates multiple univariate skeletons that capture the functional relationship between each variable and the system’s response. These skeletons are systematically merged using evolutionary approaches, ensuring interpretability throughout the process. The method was evaluated on problems with controlled and varying degrees of noise, demonstrating lower or comparable interpolation and extrapolation errors compared to two GP-based and two neural SR methods. Unlike these methods, this approach consistently learned expressions that matched the original mathematical structure.