Power grids are critical infrastructures of paramount importance to modern society and, therefore, engineered to operate under diverse conditions and failures. The ongoing energy transition poses new challenges for the decision-makers and system operators. Therefore, we must develop grid analysis algorithms to ensure reliable operations. These key tools include power flow analysis and system security analysis, both needed for effective operational and strategic planning. The literature review shows a growing trend of machine learning (ML) models that perform these analyses effectively. In particular, Graph Neural Networks (GNNs) stand out in such applications because of the graph-based structure of power grids.

The growing scale of power systems and the increasing uncertainty introduced by renewable energy sources necessitates novel optimization techniques that are significantly faster and more accurate than existing methods. The AC Optimal Power Flow (AC-OPF) problem, a core component of power grid optimization, is often approximated using linearized DC Optimal Power Flow (DC-OPF) models for computational tractability, albeit at the cost of suboptimal and inefficient decisions. To address these limitations, we propose a novel deep learning-based framework for network equivalency that enhances DC-OPF to more closely mimic the behavior of AC-OPF. The approach utilizes recent advances in differentiable optimization, incorporating a neural network trained to predict adjusted nodal shunt conductances and branch susceptances in order to account for nonlinear power flow behavior. The model can be trained end-to-end using modern deep learning frameworks by leveraging the implicit function theorem. Results demonstrate the framework's ability to significantly improve prediction accuracy.

Prior-data fitted networks (PFNs) are a promising alternative to time-consuming Gaussian process (GP) inference for creating fast surrogates of physical systems. PFN reduces the computational burden of GP-training by replacing Bayesian inference in GP with a single forward pass of a learned prediction model. We introduce Decoupled-V alue Attention (DV A)- motivated by the GP property that the function space is fully characterized by the kernel over inputs and the predictive mean is a weighted sum of training targets. DV A computes similarities from inputs only and propagates labels solely through values. Thus, the proposed DV A mirrors the GP update while remaining kernel-free. We demonstrate that PFNs are backbone architecture invariant and the crucial factor for scaling PFNs is the attention rule rather than the architecture itself. Specifically, our results demonstrate that (a) localized attention consistently reduces out-of-sample validation loss in PFNs across different dimensional settings, with validation loss reduced by more than 50% in five-and ten-dimensional cases, and (b) the role of attention is more decisive than the choice of backbone architecture, showing that CNN, RNN and LSTM-based PFNs can perform at par with their Transformer-based counterparts. Bayesian inference provides a powerful framework for reasoning under uncertainty, with methods like Gaussian processes (GPs) offering well-calibrated predictions and principled uncertainty estimates (Williams & Rasmussen, 2006). However, the practical application of these methods is often hindered by the heavy computational burden of learning kernel hyperparameters. For example, exact GP inference scales cubically with the number of data points, making its deployment infeasible for large datasets or problems requiring repeated training. Consider a physical system where a surrogate GP is chosen due to its uncertainty estimates and differentiable closed-form expressions. However, the underlying input dataset and configuration changes frequently, and the surrogate is supposed to work for these new, previously unseen variations. In such conditions, GP needs to be trained repeatedly, incurring significant computing cost, each time the dataset changes.

Therefore, developing grid analysis algorithms is important for supporting reliable operations.

Learning to optimize (L2O) parametric approximations of AC optimal power flow (AC-OPF) solutions offers the potential for fast, reusable decision-making in real-time power system operations. However, the inherent nonconvexity of AC-OPF results in challenging optimization landscapes, and standard learning approaches often fail to converge to feasible, high-quality solutions. This work introduces a \textit{homotopy-guided self-supervised L2O method} for parametric AC-OPF problems. The key idea is to construct a continuous deformation of the objective and constraints during training, beginning from a relaxed problem with a broad basin of attraction and gradually transforming it toward the original problem. The resulting learning process improves convergence stability and promotes feasibility without requiring labeled optimal solutions or external solvers. We evaluate the proposed method on standard IEEE AC-OPF benchmarks and show that homotopy-guided L2O significantly increases feasibility rates compared to non-homotopy baselines, while achieving objective values comparable to full OPF solvers. These findings demonstrate the promise of homotopy-based heuristics for scalable, constraint-aware L2O in power system optimization.

Abstract--This paper studies optimization proxies--machine learning (ML) models trained to efficiently predict optimal solutions for AC Optimal Power Flow (ACOPF) problems. While promising, optimization proxy performance heavily depends on training data quality. T o address this limitation, this paper introduces a novel active sampling framework for ACOPF optimization proxies designed to generate realistic and diverse training data. The framework actively explores varied, flexible problem specifications reflecting plausible operational realities. More importantly, the approach uses optimization-specific quantities (active constraint sets) that better capture the salient features of an ACOPF that lead to the optimal solution. Numerical results show superior generalization over existing sampling methods with an equivalent training budget, significantly advancing the state-of-practice for trustworthy ACOPF optimization proxies.

Network topology optimization (NTO) via busbar splitting can mitigate transmission grid congestion and reduce redispatch costs. However, solving this mixed-integer non-linear problem for large-scale systems in near-real-time is currently intractable with existing solvers. Machine learning (ML) approaches have emerged as a promising alternative, but they have limited generalization to unseen topologies, varying operating conditions, and different systems, which limits their practical applicability. This paper formulates NTO for congestion management problem considering linearized AC PF, and proposes a graph neural network (GNN)-accelerated approach. We develop a heterogeneous edge-aware message passing NN to predict effective busbar splitting actions as candidate NTO solutions. The proposed GNN captures local flow patterns, achieves generalization to unseen topology changes, and improves transferability across systems. Case studies show up to 4 orders-of-magnitude speed-up, delivering AC-feasible solutions within one minute and a 2.3% optimality gap on the GOC 2000-bus system. These results demonstrate a significant step toward near-real-time NTO for large-scale systems with topology and cross-system generalization.

Solving the nonlinear AC optimal power flow (AC OPF) problem remains a major computational bottleneck for real-time grid operations. In this paper, we propose a residual learning paradigm that uses fast DC optimal power flow (DC OPF) solutions as a baseline, and learns only the nonlinear corrections required to provide the full AC-OPF solution. The method utilizes a topology-aware Graph Neural Network with local attention and two-level DC feature integration, trained using a physics-informed loss that enforces AC power-flow feasibility and operational limits. Evaluations on OPFData for 57-, 118-, and 2000-bus systems show around 25% lower MSE, up to 3X reduction in feasibility error, and up to 13X runtime speedup compared to conventional AC OPF solvers. The model maintains accuracy under N-1 contingencies and scales efficiently to large networks. These results demonstrate that residual learning is a practical and scalable bridge between linear approximations and AC-feasible OPF, enabling near real-time operational decision making.

AC Optimal Power Flow (ACOPF) is computationally expensive for large-scale power systems, with conventional solvers requiring prohibitive solution times. Machine learning approaches offer computational speedups but struggle with scalability and topology adaptability without expensive retraining. To enable scalability across grid sizes and adaptability to topology changes, we propose a Hybrid Heterogeneous Message Passing Neural Network (HH-MPNN). HH-MPNN models buses, generators, loads, shunts, transmission lines and transformers as distinct node or edge types, combined with a scalable transformer model for handling long-range dependencies. On grids from 14 to 2,000 buses, HH-MPNN achieves less than 1% optimality gap on default topologies. Applied zero-shot to thousands of unseen topologies, HH-MPNN achieves less than 3% optimality gap despite training only on default topologies. Pre-training on smaller grids also improves results on a larger grid. Computational speedups reach 1,000x to 10,000x compared to interior point solvers. These results advance practical, generalizable machine learning for real-time power system operations.