# Gradient Networks for Universal Magnetic Modeling of Synchronous Machines

arXiv: https://arxiv.org/abs/2602.14947 · HTML: https://mlsanity.com/paper/2602.14947/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 45 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Builds on (most cited first, 6 of 6)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)
- [Squareplus: A Softplus-Like Algebraic Rectifier](https://mlsanity.com/paper/2112.11687/) (2021)

## Abstract (arXiv)

This paper presents a physics-constrained neural network framework for magnetic modeling of saturable synchronous machines, including spatial harmonics. By embedding gradient networks into the machine equations to model conservative electromagnetic behavior, the framework satisfies reciprocity and energy conservation by construction, while universally approximating any physically feasible magnetic characteristic. Unlike lookup tables and black-box neural networks, it guarantees monotonicity, invertibility, and smooth outputs, and remains highly data efficient. The method is validated using measured and finite-element method (FEM) data from a 5.6-kW permanent-magnet (PM) synchronous reluctance machine, and is demonstrated in real-time closed-loop control on an embedded platform. The results confirm accurate, physically consistent, and computationally efficient performance.