Multiobjective Optimization of Air-Core HTS Pancake Coils Using Machine-Learning Surrogate and Sobol-Assisted PSO for Air-Core HTS Coil Design

Designing air-core high-temperature superconducting (HTS) pancake coils for AC operation involves competing objectives and requires systematic optimization. This paper presents a novel surrogate-assisted framework that couples a pretrained feed-forward neural network (FFNN) with Sobol-assisted particle swarm optimization (PSO) and demonstrates it in four application-driven scenarios: an equal-weight case with balanced priorities across all objectives, an AC-reactor case emphasizing AC-loss reduction, a magnet case emphasizing coil-center magnetic flux, and an inductive fault current limiter case emphasizing peak stored magnetic energy. The FFNN surrogate is trained and validated using 2,700 COMSOL 2D- axisymmetric homogenous T–A simulations. The FFNN is used only to predict the expensive objective, AC transport loss per cycle, while the remaining objectives are computed analytically from the design variables: total tape length, coil volume, coil-center magnetic flux density, and inductance, where inductance is polynomial-calibrated to match COMSOL and then used to estimate peak stored magnetic energy. Sobol sequences initialize the PSO swarm and, after convergence, generate an independent 2,200-point Sobol scan for trade-off post-processing, Top 10 reporting (weighted-sum and diversity-selected), and normalized Chebyshev (min–max) compromise selection. With equal weights, the workflow matches FEM with mean relative errors of 0.07% (AC loss), 1.03% (center magnetic flux density), and 5.42% (peak stored magnetic energy).