Misha Padidar

Misha Padidar, Teresa Huang, Andrew Giuliani et al.

Stellarators are a prospective class of fusion-based power plants that confine a hot plasma with three-dimensional magnetic fields. Typically framed as a PDE-constrained optimization problem, stellarator design is a time-consuming process that can take hours to solve on a computing cluster. Developing fast methods for designing stellarators is crucial for advancing fusion research. Given the recent development of large datasets of optimized stellarators, machine learning approaches have emerged as a potential candidate. Motivated by this, we present an open inverse problem to the machine learning community: to rapidly generate high-quality stellarator designs which have a set of desirable characteristics. As a case study in the problem space, we train a conditional diffusion model on data from the QUASR database to generate quasisymmetric stellarator designs with desirable characteristics (aspect ratio and mean rotational transform). The diffusion model is applied to design stellarators with characteristics not seen during training. We provide evaluation protocols and show that many of the generated stellarators exhibit solid performance: less than 5% deviation from quasisymmetry and the target characteristics. The modest deviation from quasisymmetry highlights an opportunity to reach the sub 1% target. Beyond the case study, we share multiple promising avenues for generative modeling to advance stellarator design.

Misha Padidar, Xinran Zhu, Leo Huang et al.

Gaussian processes with derivative information are useful in many settings where derivative information is available, including numerous Bayesian optimization and regression tasks that arise in the natural sciences. Incorporating derivative observations, however, comes with a dominating $O(N^3D^3)$ computational cost when training on $N$ points in $D$ input dimensions. This is intractable for even moderately sized problems. While recent work has addressed this intractability in the low-$D$ setting, the high-$N$, high-$D$ setting is still unexplored and of great value, particularly as machine learning problems increasingly become high dimensional. In this paper, we introduce methods to achieve fully scalable Gaussian process regression with derivatives using variational inference. Analogous to the use of inducing values to sparsify the labels of a training set, we introduce the concept of inducing directional derivatives to sparsify the partial derivative information of a training set. This enables us to construct a variational posterior that incorporates derivative information but whose size depends neither on the full dataset size $N$ nor the full dimensionality $D$. We demonstrate the full scalability of our approach on a variety of tasks, ranging from a high dimensional stellarator fusion regression task to training graph convolutional neural networks on Pubmed using Bayesian optimization. Surprisingly, we find that our approach can improve regression performance even in settings where only label data is available.