Learning the Intrinsic Dimensionality of Fermi-Pasta-Ulam-Tsingou Trajectories: A Nonlinear Approach using a Deep Autoencoder Model

arXiv:2601.19567v3 Announce Type: replace-cross Abstract: We address the intrinsic dimensionality (ID) of high-dimensional trajectories, comprising n_s = 4,000,000 data points, of the Fermi-Pasta-Ulam-Tsingou (FPUT) eta model with N = 32 oscillators. To this end, a deep autoencoder (DAE) is used to infer the ID in the weakly nonlinear regime where energy recurrences are observed (eta lesssim 1). We find that the trajectories lie on a nonlinear Riemannian manifold of dimension m^{ast} = 2 embedded in a 64-dimensional phase space. By contrast, principal component analysis (PCA) together with the Participation Ratio (PR) method provides only a reasonable upper bound on the ID for each value of eta. Our DAE further reveals that the ID increases to m^{ast} = 3 at eta = 1.1, coinciding with a symmetry-breaking (SB) phenomenon characteristic of the eta model, in which additional energy modes with even wave numbers k = 2, 4 become excited. Notably, the SB phenomenon cannot be detected by the linear approach provided by PCA.

Source: arXiv cs.LG | 2026-09-15