# Differentiable Optimization for Deep Learning-Enhanced DC Approximation of AC Optimal Power Flow

arXiv: https://arxiv.org/abs/2504.01970 · HTML: https://mlsanity.com/paper/2504.01970/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 22 Mar 2025.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Parallelizing the dual revised simplex method](https://mlsanity.com/paper/1503.01889/) (2015)
- [JuMP 1.0: Recent improvements to a modeling language for mathematical optimization](https://mlsanity.com/paper/2206.03866/) (2022)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch](https://mlsanity.com/paper/2112.13469/) (2021)
- [CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbations](https://mlsanity.com/paper/2403.17660/) (2024)
- [Flexible Differentiable Optimization via Model Transformations](https://mlsanity.com/paper/2206.06135/) (2022)
- [Accelerating Optimal Power Flow with GPUs: SIMD Abstraction of Nonlinear Programs and Condensed-Space Interior-Point Methods](https://mlsanity.com/paper/2307.16830/) (2023)
- [Risk-Aware Control and Optimization for High-Renewable Power Grids](https://mlsanity.com/paper/2204.00950/) (2022)
- [An Integrated Progressive Hedging and Benders Decomposition with Multiple Master Method to Solve the Brazilian Generation Expansion Problem](https://mlsanity.com/paper/2108.03143/) (2021)
- [Bucketized Active Sampling for Learning ACOPF](https://mlsanity.com/paper/2208.07497/) (2022)
- [Assessing the Cost of Network Simplifications in Long-Term Hydrothermal Dispatch Planning Models](https://mlsanity.com/paper/2107.09755/) (2021)
- [AC-Network-Informed DC Optimal Power Flow for Electricity Markets](https://mlsanity.com/paper/2410.18413/) (2024)

## Built on by (most cited first, 1 of 1)

- [Knowledge Integration in Differentiable Models: A Comparative Study of Data-Driven, Soft-Constrained, and Hard-Constrained Paradigms for Identification and Control of the Single Machine Infinite Bus System](https://mlsanity.com/paper/2602.09667/) (2026)

## Abstract (arXiv)

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.