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

ArXi:2601.19567v2 Announce Type: replace-cross 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) $\beta$ 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 ($\beta \lesssim 1$). We find that the trajectories lie on a nonlinear Riemannian manifold of dimension $m^{\ast} = 2$ embedded in a $64$-dimensional phase space.