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A Dynamic Likelihood Approach to Filtering for Advection-Diffusion Dynamics — arXiv:2406.06837

Source: arXiv (en)
Original: https://arxiv.org/abs/2406.06837
License (as archived): CC0-1.0
Archived: 2026-10-17T16:12:50.241Z
SHA-256 of the archived text: eec97daf6f46366a58d209db1b9dfee17c6ba690cbe2f7f3ca2f2baad8968dc6
Stable URL of this page: https://metraipolis.com/documento/dc_96e9dbcd87cc

How to cite

A Dynamic Likelihood Approach to Filtering for Advection-Diffusion Dynamics — arXiv:2406.06837 — arXiv (en), https://arxiv.org/abs/2406.06837 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_96e9dbcd87cc (Metraipolis archive dc_96e9dbcd87cc, sha256 eec97daf6f46366a58d209db1b9dfee17c6ba690cbe2f7f3ca2f2baad8968dc6)

BibTeX

@misc{dc96e9dbcd87cc,
  title = {A Dynamic Likelihood Approach to Filtering for Advection-Diffusion Dynamics — arXiv:2406.06837},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2406.06837},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_96e9dbcd87cc; sha256 eec97daf6f46366a58d209db1b9dfee17c6ba690cbe2f7f3ca2f2baad8968dc6},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2406.06837. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A Bayesian data assimilation scheme is formulated for advection-dominated advective and diffusive evolutionary problems, based upon the Dynamic Likelihood (DLF) approach to filtering. The DLF was developed specifically for hyperbolic problems -waves-, and in this paper, it is extended via a split step formulation, to handle advection-diffusion problems. In the dynamic likelihood approach, observations and their statistics are used to propagate probabilities along characteristics, evolving the likelihood in time. The estimate posterior thus inherits phase information. For advection-diffusion the advective part of the time evolution is handled on the basis of observations alone, while the diffusive part is informed through the model as well as observations. We expect, and indeed show here, that in advection-dominated problems, the DLF approach produces better estimates than other assimilation approaches, particularly when the observations are sparse and have low uncertainty. The added computational expense of the method is cubic in the total number of observations over time, which is on the same order of magnitude as a standard Kalman filter and can be mitigated by bounding the number of forward propagated observations, discarding the least informative data.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-28 in cs.LG).
Categorie arXiv: Dynamical Systems (math.DS) ; Machine Learning (cs.LG); Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2406.06837 — 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 2026-10-17T15:34:49.966Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-08-28?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).