SymMatika用结构重用加速数学公式发现，能同时找显式和隐式关系。
SymMatika: Structure-Aware Symbolic Discovery
- 用基因编程+可复用结构库，从优解中提取高价值子结构指导搜索
- 在Nguyen-12上达61%恢复率，远超第二名的2%
- 开源框架支持可解释建模，适合科学发现与符号回归研究者
符号回归（SR）旨在寻找描述观测数据的闭式数学表达式。现有方法多仅擅长发现显式映射（如 $y = f(oldsymbol{x})$）或隐式关系（如 $F(oldsymbol{x}, y) = 0$），缺乏兼顾二者的现代易用框架。多数方法独立评估每个候选表达式，未利用重复出现的结构模式以加速搜索。我们提出 SymMatika，一种融合多岛遗传编程与受生物序列分析启发的可复用模体库的混合符号回归算法。它从表现优异的候选式中识别高影响力子结构，并将其重新引入后续进化代际。此外，该算法采用反馈驱动的进化引擎，支持基于隐式导数度量的显式与隐式关系发现。在多个基准测试中，SymMatika 在 Nguyen 和 Feynman 基准套件上达到当前最优恢复率：在 Nguyen-12 上实现 61% 的惊人恢复率，优于次优方案的 2%；在 Feynman 方程及 57 个 SRBench 黑箱问题子集上均展现出强健的误差-复杂度帕累托前沿表现。结果表明，结构感知的进化搜索在科学发现中具有强大潜力。为促进可解释建模与符号发现研究，我们已开源完整 SymMatika 框架。
原文摘要 · Abstract (English)
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., $y = f(\mathbf{x})$) or discovering implicit relations (i.e., $F(\mathbf{x}, y)=0$), 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 on the Nguyen and Feynman benchmark suites, an impressive recovery rate of 61\% on Nguyen-12 compared to the next best 2\%, and strong placement on the error-complexity Pareto fronts on the Feynman equations and on a subset of 57 SRBench Black-box problems. 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.
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