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.

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