Orateur
Description
Linear principal component analysis (PCA) experiences an increase in the dimensionality of the latent space when it is applied to configurations that exhibit symmetries. In this study, we introduce a novel machine learning embedding, which uses spatial transformer networks and siamese networks to account for continuous and discrete symmetries, respectively. This embedding, which we term symmetry-aware PCA, will be applied to three configurations: Burger's equation exhibiting a continuous translation symmetry, flow in sudden expansion, a discrete reflexional symmetry, and Kolmogorov Flow which combines discrete shift-reflect and continuous translation symmetries. We will show a drastic increase in the number of modes required to represent given trajectories.
Simon Kneer, Taraneh Sayadi, Denis Sipp, Peter J. Schmid, Georgios Rigas