The power flow equations are non-linear multivariate equations that describe the relationship between power injections and bus voltages of electric power networks. Given a network topology, we are interested in finding network parameters with many equilibrium points. This corresponds to finding instances of the power flow equations with many real solutions. Current state-of-the art algorithms in computational algebra are not capable of answering this question for networks involving more than a small number of variables. To remedy this, we design a probabilistic reward function that gives a good approximation to this root count, and a state-space that mimics the space of power flow equations. We derive the average root count for a Gaussian model, and use this as a baseline for our RL agents. The agents discover instances of the power flow equations with many more solutions than the average baseline. This demonstrates the potential of RL for power-flow network design and analysis as well as the potential for RL to contribute meaningfully to problems that involve complex non-linear algebra or geometry. \footnote{Author order alphabetic, all authors contributed equally.

翻译：潮流方程是一组描述电力网络中功率注入与母线电压之间关系的非线性多元方程。在给定网络拓扑的情况下，我们旨在寻找具有多平衡点的网络参数。这对应于寻找具有多个实解的潮流方程实例。当前计算代数领域的最先进算法无法处理涉及少量以上变量的网络问题。为解决这一难题，我们设计了一个能较好逼近实根数量的概率奖励函数，以及一个模拟潮流方程空间的策略空间。我们推导了高斯模型下的平均根数，并将其作为强化学习智能体的基线。这些智能体发现的潮流方程实例的解数量远超过平均基线水平。这表明强化学习在潮流网络设计与分析中的潜力，以及其在涉及复杂非线性代数或几何问题中做出有意义贡献的能力。\footnote{作者按字母顺序排列，所有作者贡献相同。}