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

arXiv:2601.19567 · cond-mat.stat-mech, cs.LG · Submitted 2026-01-27 · Read on arXiv

cond-mat.stat-mech, cs.LG

Submitted: 2026-01-27

Updated: 2026-09-13

Comments: This version matches the published one in Chaos Journal. Preliminary results were presented in November 2025 at the IUPAP Conference on Computational Physics, CP2025 XXXVI, Oak Ridge National Laboratory in Oak Ridge

Journal ref: Chaos 36, 093126 (2026)

DOI: 10.1063/5.0335458

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Reconstruction Error — 23× in this paper · explained in 2 episodes
• Activation Function — 11× in this paper · explained in 1 episode
• Embeddings — 9× in this paper · explained in 2 episodes
• Adam — 7× in this paper · explained in 2 episodes
• Participation Ratio — 5× in this paper
• Generalization — 3× in this paper · explained in 13 episodes
• Intrinsic Dimension — 3× in this paper · explained in 2 episodes
• Symmetry Breaking — 3× in this paper · explained in 3 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Clustering — 1× in this paper · explained in 2 episodes
• Latent Representation — 1× in this paper · explained in 2 episodes
• Metastability — 1× in this paper · explained in 2 episodes
• Persistent Homology — 1× in this paper · explained in 3 episodes
• Point Clouds — 1× in this paper · explained in 2 episodes
• Principal Component Analysis (PCA) — 1× in this paper · explained in 4 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Low-dimensional embeddings of high-dimensional data
• Learning Geometry and Topology via Multi-Chart Flows
• TensorFlow: A system for large-scale machine learning
• SOAP: Improving and Stabilizing Shampoo using Adam
• Manifold Dimension Estimation via Local Graph Structure
• An Intrinsic Approach to Scalar-Curvature Estimation for Point Clouds

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