# Differentiable Power-Flow Optimization

arXiv: https://arxiv.org/abs/2603.28203 · HTML: https://mlsanity.com/paper/2603.28203/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 30 Mar 2026.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [A Review of Differentiable Simulators](https://mlsanity.com/paper/2407.05560/) (2024)
- [Foundation Models for the Electric Power Grid](https://mlsanity.com/paper/2407.09434/) (2024)
- [AC Power Flow Data in MATPOWER and QCQP Format: iTesla, RTE Snapshots, and PEGASE](https://mlsanity.com/paper/1603.01533/) (2016)
- [Solving AC Power Flow with Graph Neural Networks under Realistic Constraints](https://mlsanity.com/paper/2204.07000/) (2022)
- [Introducing machine learning for power system operation support](https://mlsanity.com/paper/1709.09527/) (2017)
- [Beyond Backpropagation: Optimization with Multi-Tangent Forward Gradients](https://mlsanity.com/paper/2410.17764/) (2024)
- [KCLNet: Physics-Informed Power Flow Prediction via Constraints Projections](https://mlsanity.com/paper/2506.12902/) (2025)
- [On the Equivalence of Automatic and Symbolic Differentiation](https://mlsanity.com/paper/1904.02990/) (2019)
- [Enhancing ACPF Analysis: Integrating Newton-Raphson Method with Gradient Descent and Computational Graphs](https://mlsanity.com/paper/2406.10390/) (2024)
- [A Taxonomy of Numerical Differentiation Methods](https://mlsanity.com/paper/2512.09090/) (2025)

## Abstract (arXiv)

With the rise of renewable energy sources and their high variability in generation, the management of power grids becomes increasingly complex and computationally demanding. Conventional AC-power-flow simulations, which use the Newton-Raphson (NR) method, suffer from poor scalability, making them impractical for emerging use cases such as joint transmission-distribution modeling and global grid analysis. At the same time, purely data-driven surrogate models lack physical guarantees and may violate fundamental constraints. In this work, we propose Differentiable Power-Flow (DPF), a reformulation of the AC power-flow problem as a differentiable simulation. DPF enables end-to-end gradient propagation from the physical power mismatches to the underlying simulation parameters, thereby allowing these parameters to be identified efficiently using gradient-based optimization. We demonstrate that DPF provides a scalable alternative to NR by leveraging GPU acceleration, sparse tensor representations, and batching capabilities available in modern machine-learning frameworks such as PyTorch. DPF is especially suited as a tool for time-series analyses due to its efficient reuse of previous solutions, for N-1 contingency-analyses due to its ability to process cases in batches, and as a screening tool by leveraging its speed and early stopping capability. The code is available in the authors' code repository.