# LUMINA: Foundation Models for Topology Transferable ACOPF

arXiv: https://arxiv.org/abs/2603.04300 · HTML: https://mlsanity.com/paper/2603.04300/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 4 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Heterogeneous Graph Transformer](https://mlsanity.com/paper/2003.01332/) (2020)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Decentralized Training of Foundation Models in Heterogeneous Environments](https://mlsanity.com/paper/2206.01288/) (2022)
- [Relational Graph Attention Networks](https://mlsanity.com/paper/1904.05811/) (2019)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [Foundation Models for the Electric Power Grid](https://mlsanity.com/paper/2407.09434/) (2024)
- [OPFData: Large-scale datasets for AC optimal power flow with topological perturbations](https://mlsanity.com/paper/2406.07234/) (2024)
- [DeepOPF-V: Solving AC-OPF Problems Efficiently](https://mlsanity.com/paper/2103.11793/) (2021)
- [QCQP-Net: Reliably Learning Feasible Alternating Current Optimal Power Flow Solutions Under Constraints](https://mlsanity.com/paper/2401.06820/) (2024)
- [Unlocking Multi-Task Electric Energy System Intelligence: Data Scaling Laws and Performance with Limited Fine-Tuning](https://mlsanity.com/paper/2503.20040/) (2025)
- [Residual Power Flow for Neural Solvers](https://mlsanity.com/paper/2601.09533/) (2026)

## Built on by (most cited first, 8 of 8)

- [GENCO - A Unified Neural Solver Embedded in a Development Framework for Steady-State Grid Analysis](https://mlsanity.com/paper/2608.09921/) (2026)
- [Scalable Cross-Facility Federated Learning for Scientific Foundation Models on Multiple Supercomputers](https://mlsanity.com/paper/2603.19544/) (2026)
- [Scalable Heterogeneous Graph Foundation Models for Data-Driven Optimal Power Flow in Smart Grids](https://mlsanity.com/paper/2605.23194/) (2026)
- [Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration](https://mlsanity.com/paper/2608.25095/) (2026)
- [Scaling Laws for Physics-Aware ACOPF Surrogate Learning](https://mlsanity.com/paper/2609.16282/) (2026)
- [GridSFM: A Foundation Model for Solving AC Optimal Power Flow](https://mlsanity.com/paper/2609.30173/) (2026)
- [Mycelium: A Generalizable Cross-Grid Multi-Task Model for Electrical Distribution Systems](https://mlsanity.com/paper/2609.33120/) (2026)
- [Physics-Informed but Not Physics-Consistent: Error Geometry and Subspace Projection for Neural AC Power Flow](https://mlsanity.com/paper/2610.05959/) (2026)

## Abstract (arXiv)

Foundation models in general promise to accelerate scientific computation by learning reusable representations across problem instances, yet constrained scientific systems, where predictions must satisfy physical laws and safety limits, pose unique challenges that stress conventional training paradigms. We derive design principles for constrained scientific foundation models through systematic investigation of AC optimal power flow (ACOPF), a representative optimization problem in power grid operations where power balance equations and operational constraints are non-negotiable. Through controlled experiments spanning architectures, training objectives, and system diversity, we extract three empirically grounded principles governing scientific foundation model design. These principles characterize three design trade-offs: learning physics-invariant representations while respecting system-specific constraints, optimizing accuracy while ensuring constraint satisfaction, and ensuring reliability in high-impact operating regimes. We present the LUMINA framework, including data processing and training pipelines to support reproducible research on physics-informed, feasibility-aware foundation models across scientific applications.