Scalable Heterogeneous Graph Foundation Models for Data-Driven Optimal Power Flow in Smart Grids

Power Flow (PF), Optimal Power Flow (OPF), and State Estimation (SE) are fundamental problems in power system analysis, but solving them is computationally expensive. Graph Neural Networks (GNNs) have been proposed as fast surrogates, yet existing solvers are trained for a single problem at a time, producing narrow models that must be rebuilt for each new task. We propose a more general approach: a single Heterogeneous Residual Gated Graph Convolutional Network that solves all three problems with one shared backbone. Rather than learning one mapping, the model learns a reusable representation of how the network behaves, from which PF, OPF, and SE can each be estimated. Trained jointly on the three problems across diverse topologies and loading conditions, and evaluated on the IEEE 14-bus and 118-bus systems, the shared model matches the accuracy of task-specific GNN solvers and stays robust on unseen loading levels and topologies. These results show that a single model can capture the basic operation of a power network and serve several analysis tasks at once, a first step toward a foundation model for power systems.

AC optimal power flow (ACOPF) is foundational yet computationally expensive in power grid operations, driving learning-based surrogates for large-scale grid analysis. These surrogates, however, often fail to generalize across network topologies, a critical gap for deployment on grids not seen during training and for routine operational what-if studies. We introduce LUMINA-Bench, a comprehensive benchmark suite for ACOPF surrogate learning covering multi-topology pretraining, transfer, and adaptation. The benchmark evaluates homogeneous and heterogeneous architectures under single- and multi-topology learning settings using unified metrics that capture both predictive accuracy and physics-informed constraint violations. We additionally compare constraint-aware training objectives, including MSE, augmented Lagrangian, and violation-based Lagrangian losses, to characterize accuracy-robustness trade-offs across settings. Data processing, training, and evaluation frameworks are open-sourced as the LUMINA suite to support reproducibility and accelerate future research on feasibility-aware OPF surrogates.

Single-task fine-tuning of graph neural networks (GNNs) for power grid problems exhibits a systematic failure mode: models that achieve the lowest in-distribution error degrade the most under topology shift. We term this topology overfitting: the tendency of task-specific gradient signals to encode relational structure particular to the training topologies rather than the underlying physics, causing models to fail on unseen grids despite strong in-distribution performance. To expose and address this failure mode, we introduce MxGPS (Multiplex GPS), a multiplex graph transformer that runs K task-specialised GPS branches over a shared node encoder, jointly trained on Static State Estimation (SSE) and AC Power Flow (PF) via a self-supervised pre-training and multi-task fine-tuning protocol, with a cross-branch attention module evaluated in ablation. The joint SSE+PF objective forces the shared encoder to simultaneously satisfy complementary gradient signals, preventing it from overfitting to topology-specific relational structure. Under a 3-fold sliding-window cross-validation spanning four unseen topologies (14-, 24-, 162-, and 300-bus), MxGPS attains 0% boundary violation rate (BVR) on all four zero-shot Power Flow topologies. Critically, models with substantially lower in-distribution PF error degrade by 190% to 1400% under topology shift, whereas MxGPS degrades by only 39%, an inversion that directly implicates topology overfitting as the failure mechanism rather than insufficient model capacity. With only 1.6M parameters (12x fewer than the GridFM reference baseline), MxGPS demonstrates that multi-task joint training is a principled and parameter-efficient mechanism for topology-agnostic generalisation in power grid foundation models.