发表机构
Microsoft Research（微软研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
GridSFM是一个结合预训练图神经网络与物理信息微调的基础模型，用于大规模求解交流最优潮流，在10000节点算例上实现2.45%零样本误差，并仅用100个实例适应新电网，优于专用模型。
AI 中文摘要
我们介绍了GridSFM，这是一个结合了跨电网拓扑预训练基础模型与物理信息微调的框架，用于大规模求解交流最优潮流（AC-OPF）。该模型是一个具有1500万个参数的物理启发图神经网络，在54个拓扑（包含500至4000个节点）上进行了预训练。我们的模型在10000节点算例的留出运行条件下实现了2.45%的零样本发电成本误差，且随着系统规模增大，误差没有退化。在此基础上，我们将预训练骨干网络与基于牛顿法的物理信息微调设计相结合用于潮流计算。仅使用100个已求解实例，GridSFM就能适应多达10000个节点的未见电网。我们表明，在作为热启动点部署时，它在成本和求解器迭代次数方面均优于使用更多数据训练的单一拓扑专用神经网络模型。在设计这一基础模型时，我们克服了AC-OPF可行集可能不连通的事实。这是一个阻碍任何连续神经网络逼近解映射的障碍。为此，我们提升问题维度，并用对数惩罚松弛变量放宽其约束。我们证明了由此产生的弹性可行集是可收缩的，AC-OPF极小值在显式惩罚阈值之上仍然是弹性问题的极小值，并且将近似解投影回AC-OPF可行集是适定的。我们发布了所有模型、数据和代码，以便社区能够在AC-OPF的共享起点上继续构建。
英文摘要
We introduce GridSFM, a framework that combines a pretrained foundation model across grid topologies with physics-informed fine-tuning for solving AC Optimal Power Flow (AC-OPF) at scale. It is a $15$ million parameter physics-inspired graph neural network pretrained across $54$ topologies of $500$ to $4{,}000$ buses. Our model attains a $2.45\%$ zero-shot generation-cost error on a $10{,}000$ bus case held-out operating conditions with no degradation as system size grows. Building on this, we pair the pretrained backbone with a physics-informed fine-tuning design based on Newton's method for power flow. With only $100$ solved instances, GridSFM adapts to unseen grids up to $10{,}000$ buses. We show it out performs single topology, dedicated neural network models that are trained more data, both in terms of cost and solver iterations when deployed as warm starting points. In designing this foundation model, we overcome the fact that the feasible set for AC-OPF can be disconnected. This is an obstruction that prevents any continuous neural network from approximating the solution map. To do so, we lift the problem and relax its constraints with logarithmically penalized slacks. We prove that the resulting elastic feasible set is contractible, that the AC-OPF minimizers remain minimizers of the elastic problem above an explicit penalty threshold, and that projecting an approximate solution back onto the AC-OPF feasible set is well posed. We release all models, data, and code so that the community can build on a shared starting point for AC-OPF.
Comments19 pages
