Finding the low-dimensional distribution of quasi-symmetric stellarator geometries using machine learning methods

The 'quasi-symmetric' (QS) stellarator is an attractive concept because the toroidal angular momentum of particle in it is approximately conserved, 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. We use the auto-encoder (AE) neural network to find the low-dimension parameter space (the latent space) where the coefficients of QH geometries are distributed in. It is shown that a the 3-dimensional latent space can represent the QH geometries with a reconstruction error lower than 1%. The reconstruction of both coefficients and flux surface shapes agrees well with the DESC generated QH geometries. The low-dimensional latent space is then used to predict the theoretical Rosenbluth-Hinton residual level of zonal flows, which is an important indicator of turbulent transport. We prove that it is able to use the 3 coordinates inthe latent space to predict the RH residual level, and it becomes straightforward to select geometry with high RH level and low turbulent transport.