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Patch-Based Deep Kernel Learning for Data Assimilation and Bias Correction with Extremely Sparse Observations — arXiv:2610.41596

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.41596
License (as archived): CC0-1.0
Archived: 2026-11-02T07:19:05.172Z
SHA-256 of the archived text: 4756fe3b6931c6a6ce66efc9aae8b16bf2b7c7ce1ba72573dd15ad51400c44de
Stable URL of this page: https://metraipolis.com/documento/dc_ca40a211cb2a

How to cite

Patch-Based Deep Kernel Learning for Data Assimilation and Bias Correction with Extremely Sparse Observations — arXiv:2610.41596 — arXiv (en), https://arxiv.org/abs/2610.41596 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ca40a211cb2a (Metraipolis archive dc_ca40a211cb2a, sha256 4756fe3b6931c6a6ce66efc9aae8b16bf2b7c7ce1ba72573dd15ad51400c44de)

BibTeX

@misc{dcca40a211cb2a,
  title = {Patch-Based Deep Kernel Learning for Data Assimilation and Bias Correction with Extremely Sparse Observations — arXiv:2610.41596},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.41596},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ca40a211cb2a; sha256 4756fe3b6931c6a6ce66efc9aae8b16bf2b7c7ce1ba72573dd15ad51400c44de},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.41596. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Data Assimilation (DA) reconstructs the state of a spatio-temporal system by combining sensor observations with the output of a numerical model. Since model states are high-dimensional while observations cover only a small fraction of the domain, DA is a challenging large-scale estimation problem, central to weather forecasting and oceanography. Classical variational methods such as 3D-Var rely on a hand-crafted background error covariance that assumes unbiased errors, and therefore cannot capture state-dependent correlations or systematic model biases. Moreover, their cost grows with the size of the domain. Deep learning (DL) methods can perform DA and bias correction (BC) non-linearly, but typically offer limited interpretability and no calibrated uncertainty estimates. We propose a hybrid framework that couples a convolutional neural network (CNN) with a learnable-kernel Gaussian Process (GP) to jointly perform DA and BC from extremely sparse observations. The model is trained end-to-end by maximizing the marginal log-likelihood, learns a data-driven covariance over the whole grid, and provides both the Maximum A Posteriori analysis and its uncertainty by design. A patch-based strategy reduces the $O(N^3)$ training cost of exact GPs over $N$ grid points to $O(N)$ for a fixed patch size. Inference remains exact and only requires solving a linear system whose $O(m^3)$ cost depends on the number of observations $m \ll N$, not on the domain. The learned covariance can also replace the hand-crafted one in 3D-Var, improving its accuracy without changing the variational formulation. Experiments on sea surface temperature and salinity, with both synthetic and real, extremely sparse in-situ observations, show that the framework outperforms 3D-Var, a classical GP and a competing DL model, while reducing inference time by more than 98% with respect to 3D-Var.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2610.41596 — 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 2026-11-02T07:16:57.180Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).