Title: Exploring Multi-view Symbolic Regression methods in physical sciences Show Chinese title

Title: 探索物理科学中的多视图符号回归方法

Abstract: Describing the world behavior through mathematical functions help scientists to achieve a better understanding of the inner mechanisms of different phenomena. Traditionally, this is done by deriving new equations from first principles and careful observations. A modern alternative is to automate part of this process with symbolic regression (SR). The SR algorithms search for a function that adequately fits the observed data while trying to enforce sparsity, in the hopes of generating an interpretable equation. A particularly interesting extension to these algorithms is the Multi-view Symbolic Regression (MvSR). It searches for a parametric function capable of describing multiple datasets generated by the same phenomena, which helps to mitigate the common problems of overfitting and data scarcity. Recently, multiple implementations added support to MvSR with small differences between them. In this paper, we test and compare MvSR as supported in Operon, PySR, phy-SO, and eggp, in different real-world datasets. We show that they all often achieve good accuracy while proposing solutions with only few free parameters. However, we find that certain features enable a more frequent generation of better models. We conclude by providing guidelines for future MvSR developments. Show Chinese abstract

Abstract: 通过数学函数描述世界行为有助于科学家更好地理解不同现象的内部机制。 传统上，这是通过从基本原理和仔细观察中推导出新方程来完成的。 现代替代方法是使用符号回归（SR）自动化这一过程的一部分。 SR算法在尝试强制稀疏性的同时，寻找能够充分拟合观测数据的函数，以期生成可解释的方程。 这些算法的一个特别有趣的扩展是多视图符号回归（MvSR）。 它搜索一个参数化函数，能够描述由同一现象生成的多个数据集，这有助于缓解过拟合和数据稀缺的常见问题。 最近，多个实现添加了对MvSR的支持，它们之间存在一些细微差异。 在本文中，我们在Operon、PySR、phy-SO和eggp中支持的MvSR，在不同的现实世界数据集中进行测试和比较。 我们表明，它们通常都能达到良好的准确性，同时提出仅包含少量自由参数的解决方案。 然而，我们发现某些特性能够更频繁地生成更好的模型。 最后，我们为未来的MvSR发展提供了指导方针。