Explainable Machine Learning for Surrogate Modeling Toward the Optimization of Multipulse Field Magnetization in HTS Bulks

Abstract

High-temperature superconducting (HTS) bulks can be magnetized into trapped-field magnets (TFMs) capable of generating multitesla magnetic fields. Pulsed-field magnetization (PFM), although low-cost, suffers from heat generation and complex flux dynamics. Previous studies have highlighted the strong dependence of multiPFM outcomes on pulse sequence, material parameters, and spatial field distribution. Yet, high-fidelity numerical simulations remain computationally intensive, making rapid characterization or optimization of multipulse strategies difficult for iterative design. This article introduces an explainable machine learning (ML) framework to develop fast and accurate surrogate models for PFM characterization in HTS bulks, providing a basis for future pulse-sequence design and magnetization optimization. Using a previously validated axisymmetric electromagnetic–thermal model as the data source, an XGBoost surrogate model was constructed capable of predicting the final trapped-field response across a range of five-pulse amplitude combinations under fixed material parameters, cooling condition, pulse waveform, and interpulse interval. To provide explainability, interpretability, and physical insight, Shapley additive explanations (SHAP) analysis is employed to quantify the contribution of each input parameter and to reveal nonlinear interactions that govern multipulse strategies. The proposed surrogate model achieves orders-of-magnitude speed-up while retaining high predictive accuracy, enabling efficient search of pulse sequences. SHAP results reveal that the early pulse amplitudes dominate the prediction of the final trapped field, offering a transparent link between ML predictions and underlying superconducting physics. This explainable artificial intelligence methodology provides a powerful complementary tool to numerical simulation, supporting rapid design, understanding, and optimization of PFM processes in HTS bulks for superconducting applications.