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When Latent Dynamics Meet Data Assimilation: A Benchmark of Koopman-Type Representations — arXiv:2611.03916

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.03916
License (as archived): CC0-1.0
Archived: 2026-11-04T12:39:23.066Z
SHA-256 of the archived text: a8b8dd81d5974f181d2b4cc0f625ef6e4b460684db365e5e9857a63202b5ca58
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How to cite

When Latent Dynamics Meet Data Assimilation: A Benchmark of Koopman-Type Representations — arXiv:2611.03916 — arXiv (en), https://arxiv.org/abs/2611.03916 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_09f8cb5477fa (Metraipolis archive dc_09f8cb5477fa, sha256 a8b8dd81d5974f181d2b4cc0f625ef6e4b460684db365e5e9857a63202b5ca58)

BibTeX

@misc{dc09f8cb5477fa,
  title = {When Latent Dynamics Meet Data Assimilation: A Benchmark of Koopman-Type Representations — arXiv:2611.03916},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.03916},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_09f8cb5477fa; sha256 a8b8dd81d5974f181d2b4cc0f625ef6e4b460684db365e5e9857a63202b5ca58},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.03916. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Koopman representations describe nonlinear dynamics through linear evolution in a transformed space, offering an attractive framework for their linear simplicity and generality. Yet these advantages do not necessarily translate into improved performance in deep latent data assimilation (LDA). We systematically compare seven representative methods and structural baselines across five systems spanning approximately periodic to strongly chaotic dynamics and a broad range of state dimensions. We evaluate forecast and assimilation accuracy, physical state recovery, latent-trajectory behavior, and dynamical consistency, and assess Gaussian error assumptions, objective convexity, and uniqueness of analysis solutions. Our results reveal a trade-off between representational flexibility and optimization tractability. Linear evolution of the latent state can stabilize short-term forecasts but restrict expressiveness in strongly chaotic and high-dimensional systems, without consistently improving assimilation accuracy. Parameterized linear operators offer greater flexibility, yet their joint optimization with the encoder--decoder remains nonconvex. Methods with closed-form analysis updates generally perform better and exhibit greater robustness in our experiments, although matrix inversion remains a computational bottleneck. These findings show that the practical benefits of Koopman structure depend on both sufficient observational information and the choice of assimilation procedure.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2611.03916 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T12:29:47.254Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).