Efficient modeling of High Temperature Superconductors (HTS) is crucial for real-time quench monitoring; however, full-order electromagnetic simulations remain prohibitively costly due to the strong nonlinearities. Conventional reduced-order methods, such as the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), alleviate this cost but are limited by intrusive implementation and by the need for many interpolation points. 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. Benchmark results show that the Neural ODE outperforms POD-DEIM in both efficiency and accuracy, highlighting its potential for real-time superconducting simulations.

翻译：高温超导体（HTS）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，全阶电磁仿真仍然成本高昂，难以实现。传统的降阶方法，如本征正交分解（POD）和离散经验插值法（DEIM），虽然能缓解这一成本，但受限于侵入式实现方式以及对大量插值点的需求。本研究探讨了针对高温超导体系统积分方程法（IEM）的降阶策略。我们首次将POD-DEIM应用于基于IEM的高温超导体模型，并引入一种结构化神经常微分方程（Neural ODE）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，该神经常微分方程方法在效率和精度上均优于POD-DEIM，凸显了其在实时超导仿真中的应用潜力。