用能量梯度流训练神经网络，直接求解电力系统最优潮流。
Neural Network Optimal Power Flow via Energy Gradient Flow and Unified Dynamics
- 将最优潮流转为能量最小化问题，通过梯度流引导网络学习
- 无监督训练，不依赖标注数据，直接最小化物理残差
- 适合电力系统实时调度，兼顾精度与物理一致性
最优潮流（OPF）是电力系统运行与规划的核心优化问题，旨在最小化发电成本的同时满足功率平衡方程、机组出力限值和电压限值等物理约束。传统求解方法如内点法、序列二次规划等存在计算效率低、对初值敏感、难以批量求解等问题。现有基于深度学习的OPF方法多依赖监督学习，需预先求解大量案例，且难以保证物理一致性。本文提出一种基于神经网络动力学与能量梯度流的OPF求解方法，将OPF问题转化为能量函数最小化问题。通过构建能量函数衡量解偏离约束流形的程度，并利用梯度流引导网络学习同时满足功率平衡与成本最小化的最优解。神经网络采用无监督方式训练，直接最小化物理残差，无需标签数据，实现真正的端到端物理约束学习。
原文摘要 · Abstract (English)
Optimal Power Flow (OPF) is a core optimization problem in power system operation and planning, aiming to minimize generation costs while satisfying physical constraints such as power flow equations, generator limits, and voltage limits. Traditional OPF solving methods typically employ iterative optimization algorithms (such as interior point methods, sequential quadratic programming, etc.), with limitations including low computational efficiency, initial value sensitivity, and low batch computation efficiency. Most existing deep learning-based OPF methods rely on supervised learning, requiring pre-solving large numbers of cases, and have difficulty guaranteeing physical consistency. This paper proposes an Optimal Power Flow solving method based on neural network dynamics and energy gradient flow, transforming OPF problems into energy minimization problems. By constructing an energy function to measure the degree of deviation from the constraint manifold, and guiding networks to learn optimal solutions that simultaneously satisfy power flow constraints and minimize costs through gradient flow. Neural networks are trained unsupervised by directly minimizing physical residuals, requiring no labeled data, achieving true "end-to-end" physics-constrained learning.
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