A deep learning framework for feature selection and dimensional analysis: Variational explainable neural networks

Feature selection is one of the first steps in any data analysis and modelling activity. Choosing the wrong relevant quantities to investigate a given problem can compromise the inference process. The complexity of this task motivates efforts to harness the potential of deep learning to address it. Unfortunately, connectivist tools often struggle to converge on the correct variables. In this work, a new deep learning architecture with a variational layer is presented. The developed algorithms outperform traditional techniques, as shown by a series of numerical tests, covering the most used classes of models. The selection is not only more reliable but also more interpretable. The robustness against noise and the capability of handling sparse data have been investigated in detail. The proposed variational networks can be deployed to perform feature extraction as well and have a particular competitive advantage in applications to high dimensional data. A specific architecture has been developed for dimensional analysis, with the aim of identifying the most suitable dimensionless quantities to model the phenomena under study. The potential of the proposed techniques is confirmed by the analysis of various experimental databases, covering different branches of physics and engineering.