Efficient modeling of High Temperature Superconductors (HTSs) is crucial for real-time quench monitoring; however, full-order electromagnetic simulations remain prohibitively costly due to the strong nonlinearities. Conventional projection-based reduced-order modeling pipelines for nonlinear problems, such as Proper Orthogonal Decomposition (POD)-Discrete Empirical Interpolation Method (DEIM), alleviate this cost but often require intrusive access to the Full Order Model (FOM) operators and a substantial number of interpolation points for hyperreduction. This work investigates reduced-order strategies for Integral Equation Method (IEM) of (HTS) systems. We present the first application of POD-DEIM to IEM-based HTS models, and introduce a Structured Neural Ordinary Differential Equation (Neural ODE) approach that learns nonlinear dynamics directly in the reduced space. The benchmark results show that Neural ODE outperforms POD-DEIM both in efficiency and accuracy, highlighting its potential for real-time simulations of superconductors.

翻译：高温超导体的高效建模对于实时失超监测至关重要；然而，由于强烈的非线性特性，全阶电磁仿真仍然因计算成本过高而难以实现。针对非线性问题的传统基于投影的降阶建模流程（如本征正交分解-离散经验插值方法）虽能降低计算成本，但通常需要侵入式访问全阶模型算子，且需要大量插值点进行超约简。本研究探讨了高温超导系统积分方程法的降阶策略。我们首次将POD-DEIM方法应用于基于IEM的高温超导模型，并提出一种结构化神经常微分方程方法，该方法直接在降维空间中学习非线性动力学。基准测试结果表明，神经ODE方法在效率和精度上均优于POD-DEIM，彰显了其在超导体实时仿真中的应用潜力。