# The DESC Stellarator Code Suite Part III: Quasi-symmetry optimization

arXiv: https://arxiv.org/abs/2204.00078 · HTML: https://mlsanity.com/paper/2204.00078/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2022.

## Built on by (most cited first, 3 of 3)

- [Unsupervised Discovery of Inertial-Fusion Plasma Physics using Differentiable Kinetic Simulations and a Maximum Entropy Loss Function](https://mlsanity.com/paper/2206.01637/) (2022)
- [Improving ideal MHD equilibrium accuracy with physics-informed neural networks](https://mlsanity.com/paper/2507.03119/) (2025)
- [A proof-of-concept for automated AI-driven stellarator coil optimization with in-the-loop finite-element calculations](https://mlsanity.com/paper/2603.15240/) (2026)

## Abstract (arXiv)

The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to automatic differentiation, which efficiently provides exact derivative information. A Gauss-Newton trust-region optimization method uses second-order derivative information to take large steps in parameter space and converges rapidly. With just-in-time compilation and GPU portability, high-dimensional stellarator optimization runs take orders of magnitude less computation time with DESC compared to other approaches. This paper presents the theory of the DESC fixed-boundary local optimization algorithm along with demonstrations of how to easily implement it in the code. Example quasi-symmetry optimizations are shown and compared to results from conventional tools. Three different forms of quasi-symmetry objectives are available in DESC, and their relative advantages are discussed in detail. In the examples presented, the triple product formulation yields the best optimization results in terms of minimized computation time and particle transport. This paper concludes with an explanation of how the modular code suite can be extended to accommodate other types of optimization problems.