Symmetry-Aware Autoencoders: s-PCA and s-nlPCA
From MaRDI portal
Publication:6382213
arXiv2111.02893MaRDI QIDQ6382213
Author name not available (Why is that?)
Publication date: 4 November 2021
Abstract: 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. The spatial transformer network discovers the optimal slicing template for continuous translations so that invariant samples are aligned in the homogeneous direction. Thus, the proposed symmetry-aware autoencoder is invariant to predetermined input transformations. This embedding can be employed with both linear and nonlinear reduction methods, which we term symmetry-aware PCA (s-PCA) and symmetry-aware NLPCA (s-NLPCA). We apply the proposed framework to the Kolmogorov flow to showcase the capabilities for a system exhibiting both a continuous symmetry as well as discrete symmetries.
Has companion code repository: https://github.com/simonkneer/Symmetry-Aware-Autoencoding
No records found.
This page was built for publication: Symmetry-Aware Autoencoders: s-PCA and s-nlPCA
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6382213)
