# Improving ideal MHD equilibrium accuracy with physics-informed neural networks

arXiv: https://arxiv.org/abs/2507.03119 · HTML: https://mlsanity.com/paper/2507.03119/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 65 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Builds on (most cited first, 9 of 9)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks](https://mlsanity.com/paper/2402.00326/) (2024)
- [Deep neural network Grad-Shafranov solver constrained with measured magnetic signals](https://mlsanity.com/paper/1911.02882/) (2019)
- [Multimodal Super-Resolution: Discovering hidden physics and its application to fusion plasmas](https://mlsanity.com/paper/2405.05908/) (2024)
- [The DESC Stellarator Code Suite Part II: Perturbation and continuation methods](https://mlsanity.com/paper/2203.15927/) (2022)
- [The DESC Stellarator Code Suite Part III: Quasi-symmetry optimization](https://mlsanity.com/paper/2204.00078/) (2022)
- [Magnetic Fields with General Omnigenity](https://mlsanity.com/paper/2305.08026/) (2023)
- [Stellarator Optimization with Constraints](https://mlsanity.com/paper/2403.11033/) (2024)

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

- [Narrow Operator Models of Stellarator Equilibria in Fourier Zernike Basis](https://mlsanity.com/paper/2510.13521/) (2025)

## Abstract (arXiv)

We present a novel approach to compute three-dimensional Magnetohydrodynamic equilibria by parametrizing Fourier modes with artificial neural networks and compare it to equilibria computed by conventional solvers. The full nonlinear global force residual across the volume in real space is then minimized with first order optimizers. Already,we observe competitive computational cost to arrive at the same minimum residuals computed by existing codes. With increased computational cost,lower minima of the residual are achieved by the neural networks,establishing a new lower bound for the force residual. We use minimally complex neural networks,and we expect significant improvements for solving not only single equilibria with neural networks,but also for computing neural network models valid over continuous distributions of equilibria.