# Narrow Operator Models of Stellarator Equilibria in Fourier Zernike Basis

arXiv: https://arxiv.org/abs/2510.13521 · HTML: https://mlsanity.com/paper/2510.13521/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 39 references that are in the map.
- First posted on arXiv 15 Oct 2025.

## Builds on (most cited first, 4 of 4)

- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [The DESC Stellarator Code Suite Part II: Perturbation and continuation methods](https://mlsanity.com/paper/2203.15927/) (2022)
- [Improving ideal MHD equilibrium accuracy with physics-informed neural networks](https://mlsanity.com/paper/2507.03119/) (2025)

## Abstract (arXiv)

Numerical computation of the ideal Magnetohydrodynamic (MHD) equilibrium magnetic field is at the base of stellarator optimisation and provides the starting point for solving more sophisticated Partial Differential Equations (PDEs) like transport or turbulence models. Conventional approaches solve for a single stationary point of the ideal MHD equations, which is fully defined by three invariants and the numerical scheme employed by the solver. We present the first numerical approach that can solve for a continuous distribution of equilibria with fixed boundary and rotational transform, varying only the pressure invariant. This approach minimises the force residual by optimising parameters of multilayer perceptrons (MLP) that map from a scalar pressure multiplier to the Fourier Zernike basis as implemented in the modern stellarator equilibrium solver DESC.