Learning effective good variables from physical data
This work addresses the challenge of extracting meaningful variable combinations from physical datasets, which is incremental as it builds on existing machine learning techniques for data analysis in physics.
The paper tackles the problem of discovering effective variable groups from physical data by introducing two machine learning methods, one based on regression and the other on classification, to identify combinations of primitive variables that characterize a physical property with invariant behavior. The methods were successfully applied to empirical correlations for convective heat transfer and Newton's law of universal gravitation, demonstrating their effectiveness in finding these variable groups.
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.