Keplearn：秒级从数据中提取封闭形式数学方程的开源工具

Chandler Freeman 开发了一款名为 Keplearn 的开源符号回归引擎，使用 Rust 语言编写，旨在通过符号回归技术在秒级时间内从表格数据中提取封闭形式的数学方程 1。该软件以约翰内斯·开普勒（Johannes Kepler）命名，意在模仿他从第谷·布拉赫（Tycho Brahe）的数据中推导行星运动定律的过程 1。Keplearn 采用最佳优先递归缩减算法，具备确定性输出特性 1。其核心特点包括单二进制文件发布、零外部依赖以及在 musl 目标下完全静态编译 1。

在性能表现上，Keplearn 被纳入标准基准测试 SRBench 1。在费曼（Feynman）数据集上，该软件达到了 64.7% 的最高公开符号率，显著高于竞争对手 AIFeynman 的 55.8% 1。尽管 Keplearn 的计算预算仅为其他竞争者的一小部分，但其优势主要适用于寻找精确解析定律的场景 1。由于软件专注于提取闭合形式真值，因此在缺乏明确数学表达式的黑盒数据集上的表现可能不佳 1。

用户可通过读取 stdin 中的 TSV 或 CSV 文件使用该软件，系统将输出 JSON 格式的候选方程 1。Keplearn 的算法机制包括搜索可逆缩减链，并将常数拟合自动吸附到有理数或 pi/e/sqrt(2) 的倍数，随后通过验证确保精度 1。该项目采用 MIT 许可证发布，作者联系邮箱为 [email protected] 1。

Keplearn is an open-source symbolic regression engine written in Rust designed to extract closed-form mathematical equations from tabular data within seconds 1. Named after Johannes Kepler, the software mimics his process of deriving planetary motion laws from Tycho Brahe’s observational data 1. Developed by Chandler Freeman and released under the MIT license, Keplearn employs a best-first recursive reduction algorithm that searches for reversible reduction chains 1. The tool targets the discovery of precise analytical laws rather than general curve fitting, which may limit its effectiveness on black-box datasets lacking known closed-form ground truths 1.

The software features deterministic output generation and operates as a single binary with zero external dependencies when compiled using the musl target for full static linking 1. Functionally, it reads TSV or CSV files from standard input and outputs candidate equations in JSON format 1. During constant fitting, the algorithm automatically snaps values to rational numbers or multiples of pi, e, and sqrt(2), ensuring accuracy through verification processes 1. It also supports cross-platform installation 1.

In performance benchmarks, Keplearn achieved a 64.7% maximum public symbolic rate on the Feynman dataset within SRBench standards, significantly outperforming competitors while using only a fraction of their computational budget 1. For comparison, the AI-based method AIFeynman recorded a 55.8% symbolic rate on the same dataset 1.