We introduce “Class Symbolic Regression” (Class SR), the first framework for automatically finding a single analytical functional form that accurately fits multiple data sets—each realization being governed by its own (possibly) unique set of fitting parameters. This hierarchical framework leverages the common constraint that all the members of a single class of physical phenomena follow a common governing law. Our approach extends the capabilities of our earlier Physical Symbolic Optimization (Φ-SO) framework for symbolic regression, which integrates dimensional analysis constraints and deep reinforcement learning for unsupervised symbolic analytical function discovery from data. Additionally, we introduce the first Class SR benchmark, comprising a series of synthetic physical challenges specifically designed to evaluate such algorithms. We demonstrate the efficacy of our novel approach by applying it to these benchmark challenges and showcase its practical utility for astrophysics by successfully extracting an analytic galaxy potential from a set of simulated orbits approximating stellar streams.

中文翻译：

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类符号回归：必须适应所有这些


我们引入“类符号回归”（类 SR），这是第一个自动查找精确拟合多个数据集的单一分析函数形式的框架 - 每个实现都由其自己（可能）唯一的拟合参数集控制。这种分层框架利用了共同的约束，即同一类物理现象的所有成员都遵循共同的控制法则。我们的方法扩展了我们早期用于符号回归的物理符号优化（Φ-SO）框架的功能，该框架集成了维度分析约束和深度强化学习，用于从数据中发现无监督的符号分析函数。此外，我们还推出了首个 Class SR 基准测试，其中包括一系列专门为评估此类算法而设计的综合物理挑战。我们通过将新方法应用于这些基准挑战来展示其有效性，并通过成功地从一组近似恒星流的模拟轨道中提取分析星系势来展示其在天体物理学中的实用性。