发表机构
Inria; CNRS; Grenoble INP; IRD; INRAE（法国国家信息与自动化研究所; 法国国家科学研究中心; 格勒诺布尔国立理工学院; 法国发展研究院; 法国国家农业食品与环境研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对海洋模型次网格参数化校准中不确定性未量化的问题，提出基于仿真的推断方法，应用于单柱模型tunax的k-ε闭合系数校准，采用分块PCA汇总统计量，并证明免训练的表格基础模型方法在低预算下优于神经后验估计。
AI 中文摘要
海洋模型中垂直混合的次网格参数化依赖于无法直接测量的自由系数，必须针对高保真参考（如大涡模拟（LES））进行校准。现有方法返回点估计，而未量化相关的不确定性，这在反问题不适定或不同参数配置对数据拟合效果相当时是一个局限。基于仿真的推断（SBI）恰好解决了这一问题：给定先验并能够访问模拟器，它无需可处理的似然函数即可近似参数的全后验分布，其成本由模拟器评估次数决定。我们将其应用于基于JAX的单柱海洋模型\texttt{tunax}，以校准其$k$--$\varepsilon$闭合的系数。分块PCA汇总统计量沿深度轴压缩模拟器输出，同时保留其强迫-水平-变量结构，使得在适度的预算下推断可行。我们将神经后验估计及其序贯变体与最近基于表格基础模型的免训练方法进行比较。后者从几百次模拟器调用中恢复信息丰富的后验，在所考虑的每种预算下均优于训练过的估计器。
英文摘要
Subgrid parametrizations of vertical mixing in ocean models depend on free coefficients that cannot be measured directly and must be calibrated against high-fidelity references such as large-eddy simulations (LES). Existing approaches return point estimates and leave the associated uncertainty unquantified, a limitation when the inverse problem is ill-posed or when distinct parameter configurations fit the data comparably well. Simulation-based inference (SBI) addresses exactly this: given a prior and access to the simulator, it approximates the full posterior over parameters without requiring a tractable likelihood, at a cost set by the number of simulator evaluations. We apply it to \texttt{tunax}, a JAX-based single-column ocean model, to calibrate the coefficients of its $k$--$\varepsilon$ closure. A blockwise PCA summary statistic compresses the simulator output along the depth axis while preserving its forcing--horizon--variable structure, making inference tractable at modest budgets. We compare neural posterior estimation and its sequential variants against a recent training-free approach built on a tabular foundation model. The latter recovers informative posteriors from a few hundred simulator calls, outperforming the trained estimators at every budget considered.
