# Rethinking Neural Width for Alternating Current Optimal Power Flow Proxies

arXiv: https://arxiv.org/abs/2606.03125 · HTML: https://mlsanity.com/paper/2606.03125/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 16 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [Machine Learning for AC Optimal Power Flow](https://mlsanity.com/paper/1910.08842/) (2019)
- [A Survey on Dynamic Neural Networks for Natural Language Processing](https://mlsanity.com/paper/2202.07101/) (2022)
- [OPFData: Large-scale datasets for AC optimal power flow with topological perturbations](https://mlsanity.com/paper/2406.07234/) (2024)
- [FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees](https://mlsanity.com/paper/2506.00362/) (2025)
- [DeepOPF-V: Solving AC-OPF Problems Efficiently](https://mlsanity.com/paper/2103.11793/) (2021)
- [Physics-Informed Gradient Estimation for Accelerating Deep Learning based AC-OPF](https://mlsanity.com/paper/2502.16373/) (2025)
- [DeepOPF-U: A Unified Deep Neural Network to Solve AC Optimal Power Flow in Multiple Networks](https://mlsanity.com/paper/2309.12849/) (2023)

## Abstract (arXiv)

Deep learning proxies for Alternating Current Optimal Power Flow (ACOPF) lack systematic methods for determining architectural size. This paper conducts a constructive thought experiment to answer a fundamental inquiry: how wide must a neural network be to almost accurately approximate the ACOPF manifold? We introduce a Loss-Guided Neural Densification (LG-ND) algorithm that incrementally discovers necessary capacity by expanding only when the current deep neural network topology fails to improve further. Empirical results across various IEEE systems show that LG-ND achieves performance parity with literature baselines using up to ten times fewer neurons per layer. Such architectural minimalism is critical for the formal verification required in safety-critical grid operations.