Low-dimensional geometry learning for turbulence prediction in optimized stellarators

TL;DR

This paper demonstrates that stellarator designs with quasi-helical symmetry can be represented in a low-dimensional space using deep learning, enabling efficient turbulence prediction and optimization.

Contribution

It reveals the low-dimensional structure of stellarator geometry in a latent space, facilitating surrogate modeling and optimization of turbulent transport properties.

Findings

Stellarator designs with QH symmetry are approximately low-dimensional.

Deep learning can explicitly find the low-dimensional latent space.

Relation between linear zonal residues and axis-excursion guides optimization.

Abstract

The optimized stellarator is an attractive concept for which the averaged particle radial drift is zero, and the single particle loss can be significantly reduced. But for the reactor design, global physics such as turbulent transport also need to be optimized besides the confined single particle orbit, or properties estimated using local estimations and heuristic formulations. The first-principle global transport code is too computationally expensive to integrate into the optimization process. The fast surrogate global transport model based on machine learning is a good alternative choice, but the amount of data required to train the surrogate model is numerous due to the high degree-of-freedom of the stellarator design. The work shows that the stellarator design with quasi-helically(QH) symmetric geometry is approximately distributed in a low dimensional latent space, which can be explicitly found by deep learning. This discovery makes it possible to generate global gyrokinetic simulation data for training surrogate models to directly optimize the stellarator geometry for turbulent transport, energetic particle instability, and MHD modes. Using the low dimensional latent space and data analysis methods, the relation between linear zonal residues and axis-excursion is found, providing a simple guide to optimize low turbulent transport QH stellarators.