Global Stochastic Optimization of Stellarator Coil Configurations

TL;DR

This paper presents a novel two-step stochastic optimization method for designing stellarator coil configurations that are robust, cost-effective, and meet engineering tolerances, improving over previous local-only approaches.

Contribution

It introduces a combined global and local stochastic optimization framework using Bayesian optimization and variance-reduced local methods for stellarator coil design.

Findings

Successfully identified diverse coil configurations with minimal cost.

Achieved optimization at less than 0.1% of previous computational expense.

Demonstrated robustness and efficiency of the proposed method on W7-X-like configurations.

Abstract

In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be canceled as in the case of the National Compact Stellarator Experiment (NCSX) project [25]. Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the Sample Average Approximation and Adam, equipped with a control variate for variance reduction. Numerical experiments performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than 0.1% of the cost of previous work, which considered solely local stochastic optimization.