Overview

Symbolic regression (SR) seeks to recover closed-form mathematical expressions that describe observed data. While existing methods have advanced the discovery of either explicit mappings (i.e., $y = f(x)$) or discovering implicit relations (i.e., $F(x, y)=0$), few modern and accessible frameworks support both. Moreover, most approaches treat each expression candidate in isolation, without reusing recurring structural patterns that could accelerate search. We introduce SymMatika, a hybrid SR algorithm that combines multi-island genetic programming (GP) with a reusable motif library inspired by biological sequence analysis. SymMatika identifies high-impact substructures in top-performing candidates and reintroduces them to guide future generations. Additionally, it incorporates a feedback-driven evolutionary engine and supports both explicit and implicit relation discovery using implicit-derivative metrics. Across benchmarks, SymMatika achieves state-of-the-art recovery rates, achieving 5.1\% higher performance than the previous best results on Nguyen, the first recovery of Nguyen-12, and competitive performance on the Feynman equations. It also recovers implicit physical laws from Eureqa datasets up to 100 times faster. Our results demonstrate the power of structure-aware evolutionary search for scientific discovery. To support broader research in interpretable modeling and symbolic discovery, we have open-sourced the full SymMatika framework.

Video (Click to YouTube)

Paper

Check out our paper linked here.

Codebase

Check out our codebase at https://github.com/generalroboticslab/SymMatika for code, instructions, terminal usage, and GUI usage.

Citation

@misc{scherk2025symmatikastructureawaresymbolicdiscovery,
      title={SymMatika: Structure-Aware Symbolic Discovery}, 
      author={Michael Scherk and Boyuan Chen},
      year={2025},
      eprint={2507.03110},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2507.03110}, 
}

Acknowledgment

This work is supported by ARO under award W911NF2410405, DARPA FoundSci program under award HR00112490372, DARPA TIAMAT program under award HR00112490419, and by gift supports from BMW and OpenAI.