arXiv cs.AI· Emanuele Mele, Angelo Coluccia, Massimo Cafaro, Italo Epicoco, Paola Nassisi·· 1 天前AI 评分31
基于分块的深度核学习：用极稀疏观测做数据同化与偏差校正
Patch-Based Deep Kernel Learning for Data Assimilation and Bias Correction with Extremely Sparse Observations
AI 导读
研究者提出一种将 CNN 与可学习核高斯过程耦合的混合框架，可从极稀疏观测中联合完成数据同化与偏差校正，并通过最大化边际对数似然端到端训练。分块策略把精确 GP 在 N 个网格点上的 O(N^3) 训练成本降至 O(N)，推理仅需解一个 O(m^3) 线性系统（m 为观测数）。
正文 · 原文
Abstract: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.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.41596 [cs.AI] |
| (or arXiv:2610.41596v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.41596 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Emanuele Mele [view email]
[v1]
Fri, 30 Oct 2026 11:29:02 UTC (5,145 KB)
来源：arXiv cs.AI · arxiv.org