Learning effective good variables from physical data
Giulio Barletta Giovanni Trezza Eliodoro Chiavazzo
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.