This paper revisits datasets and evaluation criteria for Symbolic Regression,
a task of expressing given data using mathematical equations, specifically
focused on its potential for scientific discovery. Focused on a set of formulas
used in the existing datasets based on Feynman Lectures on Physics, we recreate
120 datasets to discuss the performance of symbolic regression for scientific
discovery (SRSD). For each of the 120 SRSD datasets, we carefully review the
properties of the formula and its variables to design reasonably realistic
sampling range of values so that our new SRSD datasets can be used for
evaluating the potential of SRSD such as whether or not an SR method can
(re)discover physical laws from such datasets. As an evaluation metric, we also
propose to use normalized edit distances between a predicted equation and the
ground-truth equation trees. While existing metrics are either binary or errors
between the target values and an SR model's predicted values for a given input,
normalized edit distances evaluate a sort of similarity between the
ground-truth and predicted equation trees. We have conducted experiments on our
new SRSD datasets using five state-of-the-art SR methods in SRBench and a
simple baseline based on a recent Transformer architecture. The results show
that we provide a more realistic performance evaluation and open up a new
machine learning-based approach for scientific discovery. Our datasets and code
repository are publicly available.

本研究重新审视了 Symbolic Regression 的数据集和评估标准，旨在探讨其在科学探索中的潜力。我们基于现有物理学讲义上的一组公式重建了 120 个数据集，为每个数据集设计了合理的取样范围，并提出使用标准化编辑距离作为评价指标。通过对五种最先进的 SR 方法和一种基于 Transformer 结构的简单基准线进行实验，结果表明我们提供了更现实的性能评估，并为开展基于机器学习的科学发现打开了新的思路。