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arXiv Machine Learning By Itsushi Sakata, Yuta Miyauchi, Yoshinobu Kawahara

Understanding Latent-Dimension Scaling in Dynamical-System Learning through Spectral Reliability

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The paper investigates how increasing the latent dimension in dynamical‑system learning affects rollout accuracy, using Koopman operator eigenstructure to assess spectral reliability. By comparing models trained with latent‑prediction loss versus spectral‑residual loss across six chaotic systems, the authors find that the spectral‑residual approach consistently yields lower rollout errors and longer valid prediction times, especially as dimension grows. The study demonstrates that focusing on low‑residual eigenpairs aligns better with accurate long‑term dynamics than one‑step prediction alone.

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