Generative Data-Augmented Surrogate Modelling Framework for Field Quality Improvement in ReBCO Bulk Undulators Under Limited Data Constraints

Abstract

Abstract High-temperature superconducting (HTS) bulk staggered-array undulators can generate record-breaking magnetic fields for compact light sources, but their performance is limited by non-uniform magnetic field profiles. This spatial inhomogeneity is directly related to variations in the critical current density among individual Rare-earth Barium Copper Oxide (ReBCO) bulk superconductors, which arise from microstructural inconsistencies formed during the melt-growth process. To mitigate these field errors, current state-of-the-art assembly methods rely on resource-intensive experimental pre-screening and iterative sorting of individual bulks based on their trapped field capabilities. However, predicting the exact critical current scaling factors required for an optimal spatial arrangement remains computationally demanding, a problem compounded by the limited availability and high generation cost of finite element method (FEM) training data. This paper presents a novel computational framework that integrates advanced generative data augmentation to learn underlying complex trends for producing complete artificial samples and machine learning (ML) to rapidly predict both the forward magnetic field integrals and the inverse critical current scaling factors of ReBCO bulks. To identify the optimal synthetic data generation strategy under severe data constraints, 8 deep generative architectures, encompassing adversarial, variational, and diffusion-based models, were systematically benchmarked alongside conventional statistical approaches. The utilised data synthesisers demonstrated superior synthesis of the physical manifold, achieving predictive accuracies of 99% and 88%, respectively. Ultimately, the fully augmented ML surrogate models accelerated the multidimensional FEM analyses by over 4 orders of magnitude compared to traditional numerical methods, completely bypassing the need for dedicated high-performance computing resources. The proposed framework establishes a highly data-efficient surrogate modelling approach for complex electromagnetic systems. By bridging the gap between limited simulation data and high-accuracy predictions, it provides critical computational support for the high-speed sorting and field optimisation of bulk superconductors during the experimental construction of next-generation synchrotron and free-electron laser facilities.