` 标签包裹这段。为了突出 DSSE 以及相关的名词，可以在合适的地方用 `` 进行加粗。 接着往下看，"We propose PoSE..." 这一句开始提出他们的方法。PoSE 保留了贝叶斯结构，利用流匹配（flow matching）在历史数据上训练神经网络来学习变电站注入的分布。然后还有一句 "The power flow equations..." 描述了在采样时如何通过噪声感知的卡尔曼修正引入电力潮流方程和拓扑结构。从逻辑上看，这几句都是解释 PoSE 的核心机制。由于它们是连续紧密的机制描述，可以直接放在同一个 `
` 标签内。也可以稍微拆分一下，让层次更清晰。比如第一句介绍 PoSE 是什么和学什么，第二句介绍如何利用网络方程和测量。我就把它们放在一个段落里吧，或者分成两段，看哪样排版更美观。不如分成两段，第一段讲提出PoSE及神经网络建模，第二段讲潮流方程和拓扑在采样时的作用。 再往下看，"The neural network therefore never approximates..." 这里是对 PoSE 优势的总结。它不近似电力潮流，但生成的后验样本物理一致，且一个模型能适配各种测量集。这也适合放在一个单独的 `
` 中，强调其“不近似”和“物理一致”的特点。 接下来是实验结果。在 IEEE 33-bus 测试中，相比全协方差高斯先验，PoSE 将概率注入误差（CRPS）降低了 6.7-7.5%。这是具体的数值，最好将这一句单独分出来作为实验结果的开头，也可以直接融入后文。但为了排版美观，可以独立成段。 然后是关于不确定性和覆盖率的表现。在 90% 置信区间下，PoSE 的覆盖率几乎和精确后验采样一样，而监督估计器只有 37-78%。这一段说明了 PoSE 在不确定性校准上的优越性。用 `
` 包含。 最后，在 240-bus 非平衡三相 Iowa 馈线上的表现，以及一个快速变体的表现，不仅误差最低，而且速度快（0.2-0.6秒），还能在没重新训练的情况下泛化到七种重构拓扑。这同样作为一段，用 `
` 包裹。 检查是否有列表项 `
- ` 或者引用 `
`、代码块 `
`。原文中没有这些元素，所以无需使用。 再次核对约束条件： 1. 只输出 HTML 片段，没有 Markdown 代码块，没有解释。 2. 每个自然段落用 `` 包裹。 3. 重要句子可用 ``。 4. 保留原文所有信息，绝不增删改内容。 5. 不输出 ``, `` 等标签。 好的，现在开始逐段构建 HTML。 第一段：Medium-voltage feeders... tied to one measurement set. -> `
...
` 第二段：We propose PoSE... historical data. -> `...
` 第三段：The power flow equations... Kalman-type correction. -> `...
` 第四段：The neural network therefore... and topology. -> `...
` 第五段：On the IEEE 33-bus feeder... 12 tested settings. -> `...
` 第六段：It provides reliable uncertainty... 37-78% of cases. -> `...
` 第七段：On the 240-bus... reconfigured topologies. -> `...
` 注意：原文的首字母 "Medium-voltage feeders" 首字母 M 要大写。 所有的技术名词可以稍微加粗一下，例如 `distribution system state estimation (DSSE)`, `Weighted least squares`, `supervised deep learning estimators`, `PoSE (posterior sampling for state estimation)`, `flow matching`, `noise-aware Kalman-type correction`。这有助于新闻或论文摘要的阅读。 排版草稿检查：Medium-voltage feeders have few real-time measurements, so distribution system state estimation (DSSE) rests on pseudo-measurements of the secondary substations, a prior in Bayesian terms. Weighted least squares keeps the power flow exact but reduces this prior to a mean and variance, while supervised deep learning estimators also learn the power flow and are tied to one measurement set.
We propose PoSE (posterior sampling for state estimation), which keeps the Bayesian structure of DSSE and learns only what the distribution system operator does not know, namely the distribution of substation injections, modelled by a neural network trained with flow matching on historical data.
The power flow equations, grid topology and measurements enter only at sampling, through a noise-aware Kalman-type correction.
The neural network therefore never approximates the power flow, but every posterior sample is a physically consistent operating point, and one trained prior serves any measurement set, noise level and topology.
On the IEEE 33-bus feeder, PoSE lowers the probabilistic injection error (CRPS) by 6.7-7.5% against a full-covariance Gaussian prior in all 12 tested settings.
It provides reliable uncertainty: the 90% intervals contain the true injection almost exactly as often as exact posterior samples would, whereas those of supervised estimators contain it in only 37-78% of cases.
On the 240-bus unbalanced three-phase Iowa feeder, it gives the lowest injection, voltage and branch-current errors of all estimators. A fast variant matches this accuracy at 0.2-0.6s per snapshot and, without retraining, beats Gaussian priors and retrained supervised estimators on seven reconfigured topologies.
核对文字是否完全一致，特别是标点符号和大小写： "Medium-voltage feeders have few real-time measurements, so distribution system state estimation (DSSE) rests on pseudo-measurements of the secondary substations, a prior in Bayesian terms. Weighted least squares keeps the power flow exact but reduces this prior to a mean and variance, while supervised deep learning estimators also learn the power flow and are tied to one measurement set." -> 完全一致 "We propose PoSE (posterior sampling for state estimation), which keeps the Bayesian structure of DSSE and learns only what the distribution system operator does not know, namely the distribution of substation injections, modelled by a neural network trained with flow matching on historical data." -> 完全一致 "The power flow equations, grid topology and measurements enter only at sampling, through a noise-aware Kalman-type correction." -> 完全一致 "The neural network therefore never approximates the power flow, but every posterior sample is a physically consistent operating point, and one trained prior serves any measurement set, noise level and topology." -> 完全一致 "On the IEEE 33-bus feeder, PoSE lowers the probabilistic injection error (CRPS) by 6.7-7.5% against a full-covariance Gaussian prior in all 12 tested settings." -> 完全一致 "It provides reliable uncertainty: the 90% intervals contain the true injection almost exactly as often as exact posterior samples would, whereas those of supervised estimators contain it in only 37-78% of cases." -> 完全一致 "On the 240-bus unbalanced three-phase Iowa feeder, it gives the lowest injection, voltage and branch-current