我们提出了一种基于图形神经网络（GNN）的端到端框架，以平衡通用网格中的功率流。优化被帧为监督的顶点回归任务，其中GNN培训以预测每个网格分支的电流和功率注入，从而产生功率流量平衡。通过将电网表示为与顶点的分支的线图，我们可以培训一个更准确和强大的GNN来改变底层拓扑。此外，通过使用专门的GNN层，我们能够构建一个非常深的架构，该架构占图表上的大街区，同时仅实现本地化操作。我们执行三个不同的实验来评估：i）使用深入GNN模型时使用本地化而不是全球运营的好处和趋势; ii）图形拓扑中对扰动的弹性;和iii）能力同时在多个网格拓扑上同时培训模型以及新的看不见网格的概括性的改进。拟议的框架是有效的，而且与基于深度学习的其他求解器相比，不仅对网格组件上的物理量而且对拓扑的物理量具有鲁棒性。

This paper presents a novel probabilistic forecasting method called ensemble conformalized quantile regression (EnCQR). EnCQR constructs distribution-free and approximately marginally valid prediction intervals (PIs), which are suitable for nonstationary and heteroscedastic time series data. EnCQR can be applied on top of a generic forecasting model, including deep learning architectures. EnCQR exploits a bootstrap ensemble estimator, which enables the use of conformal predictors for time series by removing the requirement of data exchangeability. The ensemble learners are implemented as generic machine learning algorithms performing quantile regression, which allow the length of the PIs to adapt to local variability in the data. In the experiments, we predict time series characterized by a different amount of heteroscedasticity. The results demonstrate that EnCQR outperforms models based only on quantile regression or conformal prediction, and it provides sharper, more informative, and valid PIs.