Mathematical and Computational Applications Article Data Augmentation and Feature Selection for Automatic Model Recommendation in Computational Physics Thomas Daniel 1,2,* , Fabien Casenave 1 , Nissrine Akkari 1 and David Ryckelynck 2 1 SafranTech, Rue des Jeunes Bois, Châteaufort, 78114 Magny-les-Hameaux, France;
[email protected] (F.C.);
[email protected] (N.A.) 2 Centre des matériaux (CMAT), MINES ParisTech, PSL University, CNRS UMR 7633, BP 87, 91003 Evry, France;
[email protected] * Correspondence:
[email protected] Abstract: Classification algorithms have recently found applications in computational physics for the selection of numerical methods or models adapted to the environment and the state of the physical system. For such classification tasks, labeled training data come from numerical simulations and generally correspond to physical fields discretized on a mesh. Three challenging difficulties arise: the lack of training data, their high dimensionality, and the non-applicability of common data augmentation techniques to physics data. This article introduces two algorithms to address these issues: one for dimensionality reduction via feature selection, and one for data augmentation. These algorithms are combined with a wide variety of classifiers for their evaluation. When combined with a stacking ensemble made of six multilayer perceptrons and a ridge logistic regression, they enable reaching an accuracy of 90% on our classification problem for nonlinear structural mechanics. Keywords: machine learning; classification; automatic model recommendation; feature selection; data augmentation; numerical simulations Citation: Daniel, T.; Casenave, F.; Akkari, N.; Ryckelynck, D. Data Augmentation and Feature Selection 1. Introduction for Automatic Model Classification problems can be encountered in various disciplines such as handwritten Recommendation in Computational text recognition [1], document classification [2], and computer-aided diagnosis in the Physics.