Newton's Lantern: A Reinforcement Learning Framework for Finetuning AC Power Flow Warm Start Models

AC optimal power flow determines the minimum-cost generation dispatch under nonlinear power balance constraints and is solved thousands of times daily in electricity market operations. Learning a direct mapping from load conditions to OPF solutions can accelerate this computation, yet with deepening renewable penetration, a single optimal dispatch is no longer sufficient. Operators require a characterization of the distribution of feasible near-optimal solutions for risk quantification, sensitivity analysis, and multi-objective trade-off assessment. Supervised neural networks provide fast point predictions but cannot capture this conditional distribution. Diffusion-based generative models can sample diverse solutions in principle, yet existing methods operating in the raw state space exhibit degraded solution quality and fail to scale beyond medium-sized systems. We identify the root cause as the conflation of two distinct tasks within a single model. Compressing the high-dimensional OPF solution manifold is one task, and learning the conditional mapping from loads to that manifold is another. This paper presents FMOPF, a framework that resolves this conflation by decoupling compression from generation through latent flow matching and by explicitly modeling load-state coupling through a Constraint-Aware Interaction Prior Network. Experiments on four IEEE test systems demonstrate that FMOPF provides the most effective Newton-Raphson warm starts, achieves the lowest tail risk among generative methods, and is the first such method to scale to systems with several hundred buses while preserving full feasibility. Ablation studies confirm that the latent generation pipeline is a necessary condition for physical feasibility and that the interaction prior functions as a late-stage tail-risk controller.

Solving AC Optimal Power Flow (AC-OPF) is of central importance in electricity market operations, where interior-point methods (IPMs) such as IPOPT are the standard solvers. A growing body of work uses machine learning to predict primal warm-start iterates, reporting iteration reductions of 30-46%. We show that these reported gains rest on an inappropriate evaluation baseline: prior methods benchmark against the flat start $V_m = 1, V_a = 0$, whereas the solver's actual default - the variable-bound midpoint $(l+u)/2$ - is near-optimal for log-barrier centrality. Against this corrected baseline, no primal-only warm-start method reduces solver iterations. We trace the failure to a geometric property of interior-point methods: primal prediction accuracy is anticorrelated with convergence speed, and providing the ground-truth optimal solution $x^*$ without dual variables causes the solver to diverge. Oracle experiments establish that the complete primal-dual-barrier state $(x^*, λ^*, z^*, μ^*)$ reduces IPOPT iterations from 23 to 3 - an 85% reduction that is structurally inaccessible to primal-only methods. To enable rigorous evaluation of warm-start methods on this task, we release a benchmark suite comprising dual-labeled AC-OPF datasets with IPOPT-extracted solutions, a corrected evaluation protocol, and WARP - a topology-conditioned encode-process-decode interaction network that predicts the full interior-point state $(\hat{x}, \hatλ, \hat{z}, \hatμ)$ on the heterogeneous constraint graph. WARP achieves a 76% reduction in IPOPT iterations while natively accommodating N-1 contingency topology variations without retraining.

This work formulates and solves optimization problems to generate input points that yield high errors between a neural network's predicted AC power flow solution and solutions to the AC power flow equations. We demonstrate this capability on an instance of the CANOS-PF graph neural network model, as implemented by the PF$Δ$ benchmark library, operating on a 14-bus test grid. Generated adversarial points yield errors as large as 3.7 per-unit in reactive power and 0.08 per-unit in voltage magnitude. When minimizing the perturbation from a training point necessary to satisfy adversarial constraints, we find that the constraints can be met with as little as an 0.04 per-unit perturbation in voltage magnitude on a single bus. This work motivates the development of rigorous verification and robust training methods for neural network surrogate models of AC power flow.