Symmetry-Aware Autoencoders: s-PCA and s-nlPCA. (arXiv:2111.02893v3 [physics.flu-dyn] UPDATED)

Nonlinear principal component analysis (NLPCA) via autoencoders has attracted
attention in the dynamical systems community due to its larger compression rate
when compared to linear principal component analysis (PCA). These model
reduction methods experience an increase in the dimensionality of the latent
space when applied to datasets that exhibit invariant samples due to the
presence of symmetries. In this study, we introduce a novel machine learning
embedding for autoencoders, which uses Siamese networks and spatial transformer
networks to account for …

arxiv physics symmetry