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2021

Symmetry-Aware Autoencoders: s-PCA and s-nlPCA

Kneer, Simon, Sayadi, Taraneh, Sipp, Denis et al.

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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 discrete and continuous symmetries, respectively.
The Siamese branches autonomously find a fundamental domain to which all samples are transformed, without introducing human bias.

Symmetry-Aware Autoencoders: s-PCA and s-nlPCA · Around

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