# Learning Optimal Power Flow Value Functions with Input-Convex Neural Networks

arXiv: https://arxiv.org/abs/2310.04605 · HTML: https://mlsanity.com/paper/2310.04605/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 39 references that are in the map.
- First posted on arXiv 6 Oct 2023.

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

- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [Fashionable Modelling with Flux](https://mlsanity.com/paper/1811.01457/) (2018)
- [Averaging Stochastic Gradient Descent on Riemannian Manifolds](https://mlsanity.com/paper/1802.09128/) (2018)
- [Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch](https://mlsanity.com/paper/2112.13469/) (2021)
- [Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks](https://mlsanity.com/paper/2006.11029/) (2020)
- [A Convex Neural Network Solver for DCOPF with Generalization Guarantees](https://mlsanity.com/paper/2009.09109/) (2020)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Assessing the Cost of Network Simplifications in Long-Term Hydrothermal Dispatch Planning Models](https://mlsanity.com/paper/2107.09755/) (2021)
- [Benchmarking Large-Scale ACOPF Solutions and Optimality Bounds](https://mlsanity.com/paper/2203.11328/) (2022)
- [Regularized Decomposition of High-Dimensional Multistage Stochastic Programs with Markov Uncertainty](https://mlsanity.com/paper/1505.02227/) (2015)
- [The Parametric Cost Function Approximation: A new approach for multistage stochastic programming](https://mlsanity.com/paper/2201.00258/) (2022)
- [Enabling Fast Unit Commitment Constraint Screening via Learning Cost Model](https://mlsanity.com/paper/2212.00483/) (2022)

## Built on by (most cited first, 7 of 7)

- [Fast and Reliable N-k Contingency Screening with Input-Convex Neural Networks](https://mlsanity.com/paper/2410.00796/) (2024)
- [ICNN-enhanced 2SP: Leveraging input convex neural networks for solving two-stage stochastic programming](https://mlsanity.com/paper/2505.05261/) (2025)
- [Tightening optimality gap with confidence through conformal prediction](https://mlsanity.com/paper/2503.04071/) (2025)
- [Sobolev Training of End-to-End Optimization Proxies](https://mlsanity.com/paper/2505.11342/) (2025)
- [Constraint-Informed Active Learning for End-to-End ACOPF Optimization Proxies](https://mlsanity.com/paper/2511.06248/) (2025)
- [SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functions](https://mlsanity.com/paper/2604.22355/) (2026)
- [Input convex neural networks as surrogates in mathematical optimisation](https://mlsanity.com/paper/2608.09707/) (2026)

## Abstract (arXiv)

The Optimal Power Flow (OPF) problem is integral to the functioning of power systems, aiming to optimize generation dispatch while adhering to technical and operational constraints. These constraints are far from straightforward; they involve intricate, non-convex considerations related to Alternating Current (AC) power flow, which are essential for the safety and practicality of electrical grids. However, solving the OPF problem for varying conditions within stringent time frames poses practical challenges. To address this, operators resort to model simplifications of varying accuracy. Unfortunately, better approximations (tight convex relaxations) are often computationally intractable. This research explores machine learning (ML) to learn convex approximate solutions for faster analysis in the online setting while still allowing for coupling into other convex dependent decision problems. By trading off a small amount of accuracy for substantial gains in speed, they enable the efficient exploration of vast solution spaces in these complex problems.