Amortized Localized Posterior Inference for Model Calibration with Application to an Ocean Turbulence Closure

Model discrepancy may prevent a single calibration parameter from reproducing a physical response across the context domain. In addition, uncertainties in observations and contexts affect calibration and must be accounted for and quantified.

模型差异可能会阻碍单一校准参数在整个上下文域中重现物理响应。此外，观测和上下文中的不确定性会影响校准，必须对其进行核算和量化。

We construct a family of localized posteriors by weighting observation likelihoods according to their proximity to a target context. Gaussian localization weights incorporate context uncertainty through covariance inflation, with reflection at domain boundaries and an optional correction for uneven context sampling.

我们通过根据观测似然与目标上下文的接近程度对其进行加权，构建了一系列局部后验分布。高斯局部化权重通过协方差膨胀纳入了上下文不确定性，并在域边界处进行反射，同时可选择对不均匀的上下文采样进行校正。

A conditional normalizing flow approximates the family of posteriors through amortized variational inference. Integrating the localized posteriors under a prescribed context measure gives the marginalized parameter distribution.

条件归一化流通过摊销变分推理来近似这一后验分布族。在规定的上下文测度下对局部后验分布进行积分，即可得到边缘化的参数分布。

In a twin experiment with the Branin-Hoo model, we compare global and localized inference under uniform and skewed context distributions. Localization reduces the reported aggregate predictive errors relative to the global posterior.

在针对 Branin-Hoo 模型的孪生实验中，我们比较了均匀和偏态上下文分布下的全局推理与局部推理。与全局后验相比，局部化降低了报告的总体预测误差。

An application to the k-$\epsilon$ turbulence closure in a single-column ocean model, with atmospheric surface forcing as context, shows that localized posterior calibration reduces temperature and zonal-velocity errors relative to deterministic and global-posterior calibration. Both twin experiments are constructed to admit local compensation.

在单柱海洋模型中对 k-$\epsilon$ 湍流闭合的应用（以大气表面强迫作为上下文）表明，与确定性校准和全局后验校准相比，局部后验校准降低了温度和纬向速度误差。这两个孪生实验的构建均允许局部补偿。