We assume that a sufficiently large database is available, where a physical property of interest and a number of associated ruling primitive variables or observables are stored. We introduce and test two machine learning approaches to discover possible groups or combinations of primitive variables: The first approach is based on regression models whereas the second on classification models. The variable group (here referred to as the new effective good variable) can be considered as successfully found, when the physical property of interest is characterized by the following effective invariant behaviour: In the first method, invariance of the group implies invariance of the property up to a given accuracy; in the other method, upon partition of the physical property values into two or more classes, invariance of the group implies invariance of the class. For the sake of illustration, the two methods are successfully applied to two popular empirical correlations describing the convective heat transfer phenomenon and to the Newton's law of universal gravitation.

翻译：我们假设存在一个足够大的数据库，其中存储了感兴趣的物理性质以及若干相关的初始原始变量或可观测量。我们引入并测试了两种机器学习方法，以发现原始变量的可能分组或组合：第一种方法基于回归模型，第二种方法基于分类模型。当感兴趣的物理性质表现出以下有效不变行为时，变量组（此处称为新的有效良好变量）可被视为成功发现：在第一种方法中，变量组的不变性意味着物理性质在给定精度范围内具有不变性；在第二种方法中，当物理性质值被划分为两个或多个类别时，变量组的不变性意味着分类的不变性。为便于说明，这两种方法被成功应用于描述对流传热现象的两种常用经验关联式以及牛顿万有引力定律。