  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.
